If you want to give your fighter more access to magic without rebuilding you're going to be limited to skills, feats, and magical items. None of these will give your fighter heavy magical abilities, instead letting you play the character as someone who has learned basic magic.
Skills
The skills that increase magical knowledge are:
Knowledge (Arcana) - represents general knowledge your fighter has acquired about magic; what an arcane symbol means, how the local mage guild heirarchy is organized. Stuff he would learn in school or from talking to spellcasters.
Spellcraft - much more specialized knowledge about specific magical effets. While Knowledge (Arcana) is theoretical studies, this is applied studies. Being able to recognize magical effects, figure out what spells are being cast. Knowledge gained by seeing magic in action, how it's been used.
Use Magic Device - knowing how to use the magical items that are common to spellcasters; staff, wands, scrolls, etc. The Evil Necromancer has defeated the parties fighter and is now monologuing to the rest of the party about their imminent defeat. The tired fighter rolls over, grabs the wand of fireballs from the necromancers belt and make a brilliant quip as fire blossoms around them.
Feats
There aren't a lot of feats that contribute to magical abilities. The first one I recommend is Able Learner from Races of Destiny. This feat treats all skills as being in-class skills. This will allow you to level up the above skills quicker.
The other feat that is useful is Magical Training, from the Players Guide to Faerun. It allows your character to cast three 0-level arcane spells per day as either a wizard or sorcerer.
Items
Have your character carry around magical items that are commonly associated with spellcasters. Staves, scrolls, wands. Combined with Use Magic Device this allows the fighter to have access to magical abilities.
A staff is an excellent choice of a magical item for this type of fighter. They can use it as their melee weapon, and use the magical abilities within it. A great surprise tactic when fighting: thrust, thrust, parry, Cone of Cold.
Your question revolves around the mechanical quality of various options, and I will therefore give an optimizer’s perspective to the issues. I will use words like “should” or even “must” without qualification, so I am stating up front that this entire answer is qualified as applying if you want to optimize your character.
Unfortunately, your question of regular fighter vs. sneak attack thug is problematic. Because of the realities of 3.5, which favors heavy multiclassing for martial characters, this is a false dichotomy. Thus, I’m going to introduce my answer with a significant tangent into metagame theory surrounding the fighter class. I consider this critical background information to discussing the sneak attack thug.
Why take fighter levels: Feats and BAB
The fighter is a weak class; feats are all he gets. Feats are valuable, but class features are (or should be) more so. The fighter is also a full-BAB class, which may matter to you but may not. Generally, these features are most critical when it comes to qualifying for prestige classes.
Bonus feats
In core, there simply aren’t enough feats that are good enough to justify getting only feats as your class features. Outside of core, there are more than enough feats, but the alternatives to fighter get that much better. In other words, (the regular) fighter is a class you only take if you are desperate for feats and cannot lose any BAB (if you can lose BAB, cleric, monk, and psychic warrior are often more effective ways to get feats).
The only time you should be “desperate” for feats is when you want to use a prestige class that requires a lot of them.
Base attack bonus
As for BAB, it’s important but not the be-all, end-all, unless you’re aiming to enter a prestige class that has BAB as its primary “gatekeeper” (that is, you can enter the class as soon as you have enough BAB, so missing out on BAB directly delays entry into the prestige class). If you want to enter a class that requires BAB +3, but 8 ranks in a skill, missing some BAB won’t matter much because you wouldn’t be able to enter until you got the 8 ranks anyway. On the flip side, if a class requires BAB +5 but 4 ranks, missing a BAB puts you a level behind, which is a fairly big deal.
Conclusion
So ultimately, fighter is a class that is best used to ease entry into prestige classes. In low-level games, where feats are more scarce, two levels (for a feat per level) can be good, too. But usually, you get enough feats to get the ones you actually want without needing fighter levels, which means those levels are better spent elsewhere.
Reality: fighters multiclass
Because fighter levels are primarily useful for entering prestige classes, it almost goes without saying that fighters should not literally be Fighter 20. In reality, they shouldn’t actually be more than Fighter 2 most of the time; a feat-per-level is solid; a feat-every-other-level is not. But most prestige classes cannot be entered at level 3. Thus, you need other classes.
Multiclass Penalties
Most groups do not use multiclass penalties; they are ineffective at doing what they were intended for (limit multiclassing) and many groups feel that was an undesirable goal in the first place (multiclassing is one of the biggest strengths of the d20 system).
That said, as a Fighter 2, you don’t have to worry about it. You do not suffer multiclass penalties as long as all your classes are within one level of each other, which means you can be Fighter 2, Fighter 2/X 1, Fighter 2/X 2, and Fighter 2/X 3 (or Fighter 2/X 1/Y 2 or whatever) without any multiclass penalties. Prestige classes also do not count, so if you enter a prestige class at 6th, you’ll never see a penalty.
Typical options: barbarian, cleric, ranger, warblade
Barbarian and cleric are two of the best single-level dips in the game. Barbarian 1 gives Rage, and with Complete Champion, Pounce. Cleric gives a smattering of spells, two domains (which may mean two bonus feats, or things you can’t get as feats), and Turn Undead which can be used with Divine feats. Complete Champion again improves that option, adding the excellent Devotion feats as alternatives for Domains, including the fantastic Travel Devotion. Because of Pounce and Travel Devotion, basically every melee character ever should have at least one level of either barbarian or cleric if Complete Champion is in play.
If fighter is your choice for entering prestige classes that require a lot of feats as well as BAB, ranger is your choice for entering prestige classes that require a lot of skill ranks as well as BAB. Full BAB and 6+Int skills is solid. The actual ranger class features are fairly meh, but if you need any of those feats, hey, more free feats.
Warblade from Tome of Battle is an excellent class, and it multiclasses very nicely (half your non-warblade levels count towards your warblade level for the sake of the warblade’s maneuvers). It’s often seen as “what the fighter should have been,” but if you need a bunch of feats, taking fighter levels before entering warblade works quite nicely.
Sneak Attack Thug and Rogue
What I’ve established, hopefully, is that you should not compare a Sneak Attack Thug 20 to a Fighter 20; neither option is likely or desirable. Rather, you’re talking about a Fighter 2/something 3/prestige class 10/another thing 5 or something, and wondering how the sneak attack thug fits into this picture.
Some basic facts about the sneak attack thug
The Sneak Attack fighter is better in combat than a (core) rogue. He arguably gets 1d6 more Sneak Attack (thanks to the bonus feats on both 1st and 2nd level), he has full BAB so iterative attacks come online sooner. The thug is more skilled than a regular fighter by a fair margin, though far, far less so than the rogue.
But ultimately, the Sneak Attack thug’s only schtick is combat, and there are better ways to do combat than Sneak Attack. Simple example is a mounted fighter/barbarian charger with a lance and Power Attack. Another good one is the so-called horizon tripper, taking advantage of Improved Trip’s excellent lock-down by using Combat Reflexes, and comboing fighter, barbarian, and ranger in order to enter horizon walker for excellent mobility.
Considerations of the rogue
Meanwhile, the rogue is generally seen as a higher “tier” class than the fighter. In combat, the class is lackluster; Sneak Attack is non-trivial to set up, relies on feat-intensive dual-wielding for optimal damage, and even with all that it doesn’t keep up, damage-wise, with a good charger.
But the rogue is still better. All a charger can do is damage; a rogue can do so much more. The thug adds in a fair few more skills, but the class skill list is still paltry compared to the rogue’s, and the rogue probably has more than twice as many skill points. Most importantly, the rogue gets Use Magic Device in-class, and that skill is amazing.
Conclusion
If you do not need feats very badly, you don’t really want (regular) fighter levels. The sneak attack fighter replaces these with Sneak Attack; not a bad trade, but the rogue gets so much more along with Sneak Attack.
So you should only take fighter levels if you really need BAB and feats or Sneak Attack. If you’re a rogue, stick with rogue unless you need BAB for something. If you want some BAB, but aren’t hurting for feats, a sneak attack thug level will get you BAB without costing you Sneak Attack, and it’ll hurt your skills at least somewhat less. If you really need BAB and feats, then regular fighter is your best bet.
Best Answer
This is going to vary massively from game to game, but in my own games, yes, absolutely.
A gestalt game is already assuming a certain amount of changing to the classes that you are using, because you are not training discretely as one thing and then another, but rather as a homogenous whole. That is, you are not both a fighter and a cleric, you are a fighter//cleric, and what that means is left a bit undefined.
In short, if you can convince your DM/group that the combination makes sense under a given backstory, it should not be a problem. For example, though cloistered, your character might get considerable martial training. Or you might simply be a particularly cranial divine warrior. This is all about figuring out what makes sense and making a good case of it for your DM/group.