As Flenyar quoted in his answer:
Each time he gains a new level, he chooses two classes, takes the best
aspects of each and applies them to his characteristic.
This implies that if one class would gain a BAB at it's respective level, you do as well. Note that unlike normal multiclass characters, your stats do depend on what order you take the classes in.
Notice how Flenyar's progression (6 levels of Fighter/Rogue, then 4 levels of Wizard/Rogue) gives a BAB of +9, but the following progression gives you a full BAB of +10, even though the character is still a Fighter 6/Wizard 4//Rogue 10:
- Fighter 1 / Rogue 1 (+1 [Fighters gain +1 every level])
- Fighter 2 / Rogue 2 (+1 [Fighters gain +1 every level])
- Fighter 3 / Rogue 3 (+1 [Fighters gain +1 every level])
- Fighter 4 / Rogue 4 (+1 [Fighters gain +1 every level])
- Fighter 5 / Rogue 5 (+1 [Fighters gain +1 every level])
- Wizard 1 / Rogue 6 (+1 [Rogues gain +1 at 6th level])
- Wizard 2 / Rogue 7 (+1 [Both Wizards and Rogues BAB improves])
- Wizard 3 / Rogue 8 (+1 [Rogues gain +1 at 8th level])
- Fighter 6 / Rogue 9 (+1 [Fighters gain +1 every level])
- Wizard 4 / Rogue 10 (+1 [Both Wizards and Rogues BAB improves])
Total BAB at level 10 is +10.
This means that even a Wizard//Sorcerer gestalt (or any other two low BAB classes) can have a perfect BAB if you take just one level of another perfect BAB class:
- Wizard 1 / Fighter 1 (+1 [Fighters gain +1 every level])
- Wizard 2 / Sorcerer 1 (+1 [Wizards gain +1 at 2nd level])
- Wizard 3 / Sorcerer 2 (+1 [Sorcerer gain +1 at 2nd level])
- Wizard 4 / Sorcerer 3 (+1 [Wizards gain +1 at 4th level])
- Wizard 5 / Sorcerer 4 (+1 [Sorcerer gain +1 at 4th level])
- Wizard 6 / Sorcerer 5 (+1 [Wizards gain +1 at 6th level])
- Wizard 7 / Sorcerer 6 (+1 [Sorcerer gain +1 at 6th level])
- Wizard 8 / Sorcerer 7 (+1 [Wizards gain +1 at 8th level])
- Wizard 9 / Sorcerer 8 (+1 [Sorcerer gain +1 at 8th level])
- Wizard 10 / Sorcerer 9 (+1 [Wizards gain +1 at 10th level])
Total BAB at level 10 for this Wizard 10//Fighter 1/Sorcerer 9 is +10 (perfect.) This cannot be determined without the order of the levels taken.
However...
...the DM may overrule this, based on the wording of this rule:
Base Attack Bonus: Choose the better progression from the two classes. (Emphasis mine.)
It is conceivable, then, that the Wizard 10//Fighter 1/Sorcerer 9 is a character with 1 level of perfect BAB progression (+1) and 9 levels of low BAB progression (+4), leaving him with only a BAB of +5.
I'm not sure of any official errata on the matter, but it makes a big difference in some cases. Ask your DM, or make sure your players know your ruling if you are the DM. Personally, I would stick with the latter "better progression" rule over the "better increase" rule, since it seems to be the intent of gestalt.
There is also the "Fractional Base Bonuses" house rule, presented on Unearthed Arcana p.73, which is designed to allow smooth leveling of gestalt multiclass characters without any of these exploitable loopholes.
Saves
Since you mentioned saves in your comment, I'll touch on it briefly:
Saves would indeed work the same was as BAB, but beware that they are even easier to inflate artificially if you use the first presented "better increase" rule. This is because at first level of every class with good saves, that save "increases" from +0 to +2. Therefore it's even easier to end up with ridiculously high saves through multiclassing gestalt, if you don't simple lump all progression levels together before calculating character stats.
As a side note, consider two classes which gain 1d6 sneak attack every other level. Staggering them as I suggest staggering BAB increases still cannot double your sneak attack damage, since the book explicitly states:
Class features that two classes share accrue at the rate of the faster class.
Evasion doesn't stack
Unless it specifically states otherwise (and some of them do), gaining duplicates of class abilities doesn't do anything special. You just get the ability to do... something you can already do.
For things with effects based on level, like Turn Undead and Wildshape, whether or not they 'stack' with each other to determine what effective level (EL) you use the ability at is complex thing that depends on FAQ answers and the specific sources of the ability and stuff. It's a whole nother answer worth of information.
Evasion does not stack. Uncanny Dodge, another rogue ability, has a specific caveat;
If a character already has uncanny dodge from a second class, the character automatically gains improved uncanny dodge instead, and the levels from the classes that grant uncanny dodge stack to determine the minimum rogue level required to flank the character.
So a common house rule for multiple sources of Evasion is to grant the character Improved Evasion.
If you have class that grants an actual Feat, like Ranger grants the Track feat, and you already have that feat, unless the entry says 'if you already have the feat, you may pick another' or something similar, you just get.. nothing.
A common houserule is that you get to pick a different feat in those circumstances.
Even with that houserule, though, gestalt's basic rule is that if you get something from both sides of the gestalt, it overlaps, it does not stack. This is applied to BAB and saving throws explicitly, but a common houserule applies it to everything - so you can't dual-progress Sneak Attack by playing a Sneak Attack Fighter//Rogue, and you can't dual-progress your Wizard casting by playing a Wizard//Something/Loremaster.
So basically, under the rules, and under the common gestalt houserules, that character gets nothing special for getting evasion twice. Equally though, many tables grant Improved Evasion when you get Evasion twice, so you could go with that.
By RAW, you get nothing. By houserules, you could get nothing, or you could get improved evasion, or the GM might feel nice and grant a feat or a bonus to reflex saves or something. It's up to the GM, though, there is no explicit rules granting you anything at all for getting Evasion twice.
However, there is stuff that trades Evasion away
While you can't get Evasion twice by RAW, you can trade Evasion away once and still receive Evasion, such as by an Alternate Class Feature, or a Level Substitution. I'll list some of the better ones here.
- Spell Reflection [Complete Mage] - Trade evasion for the ability to reflect targeted spells that miss you.
- Dungeon Specialist [PHB II] - Trade evasion for a climb speed.
- Mettle of Mountains (Goliath Rogue Substitution Level) [Races of Stone] - Lose Evasion, gain Mettle (and bonus to Fort saves).
Best Answer
So if you are a rogue//sneak-attack fighter, for example, the answer is no. Each level, you gain the “best value” from each class. For example, a 3rd-level rogue has a +1 bonus to Fort while a 3rd-level fighter has a +3 bonus to Fort—a 3rd-level rogue//fighter has the +3 from fighter, the better number, but not +4, adding the two together. Sneak attack works the same way: at 1st level, both give +1d6, so you take the “better” value (which is +1d6 since they’re tied).
The argument starts when you consider dipping a level of something else on one side. For example, consider a rogue//barbarian/sneak-attack fighter. At 1st level, rogue give +1d6 sneak attack damage, and barbarian gives none. OK, so that’s fine, you get +1d6. At 2nd level, rogue gives no sneak attack damage, but fighter, if you’re now taking your first level of it, give +1d6—so now at 2nd level you have +2d6. At 3rd level, now rogue gives another +1d6 while fighter is “off.”
This “staggering” technique tends to be considered rather poor form, and many DMs won’t allow it. Many will argue that both rogue and sneak-attack fighter give half a sneak attack die each level (rounded up), so you don’t really gain +1d6 on one level and +0 on another, but rather gain “+½d6” each level. From this perspective, they wouldn’t stack, because there is no staggering.
On the other hand, you can do this kind of “staggering,” so to speak, without using gestalt at all (by taking 1 level in a whole bunch of classes that get +1d6 sneak attack at 1st level; yes, there are enough), which might be a point in favor of being able to do it with gestalt.
But ultimately, gestalt is a variant ruleset that is not exactly fully fleshed out, and requires DM adjudication. You need to ask your DM this question, really. For example, Unearthed Arcana doesn’t consider the ninja or scout, with their “skirmish” and “sudden strike” damage bonuses that are quite similar to sneak attack. Do those stack with sneak attack, e.g. on a rogue//scout? They are very similar, and count as one another for requirements, but by Unearthed Arcana’s rules, as written, they would. Should they? That I can’t answer—I have played games where it would be fine, I have played other games where it would be overpowered. Ask your DM.