Just about every option in the game for wielding a larger weapon is awful. A size category adds, on average, +1 damage, which is nothing, and certainly isn’t worth a feat. Damage does grow super-linearly with size, which means each size increase is worth more the more you have, but you can’t get bigger than Colossal so you can’t even really go “all in” on the idea and push the value far enough that it’d be “good.”
Monkey Grip and Wield Oversize Weapon both fall in this category and are entirely typical—i.e. bad—though of the two, taken in a vacuum, Wield Oversize Weapon is probably better, since attack bonus is worth more than damage bonus, and Wield Oversize Weapon’s bonus to attack may well exceed Monkey Grip’s bonus to damage. As you note, Wield Oversize Weapon is an epic feat, so its weakness is particularly egregious when you consider what other epic characters might be doing, but then again, this situation maybe doesn’t look so awful when you consider other mundane epic feats—Epic Weapon Focus gives the same +2 to hit, but only for a specific weapon, and that’s all it does. So you can kind of imagine what the designers were thinking when they wrote it.
The problem here is that Monkey Grip and Epic Weapon Focus are absolute garbage, and not reasonable points of comparison. No one should ever take either feat, so the question “should I take Epic Weapon Focus, Monkey Grip, or Wield Oversize Weapon?” is meaningless—those aren’t your only options. D&D 3.5e has a bajillion feats, and a whole lot of them are much better than any of these feats. You can’t even claim that you’ve run out of better feats to take, because there are definitely stronger feats that you can take as many times as you like, so you’ll never be at a point where any of these feats is the right choice.
In short, Wield Oversize Weapon is awful, and honestly comparing it against Monkey Grip, or other mundane epic feats, is being much too generous. Realistically, since it’s an epic feat, its competition is instead Epic Spellcasting—and anything that isn’t Epic Spellcasting falls far, far short. Epic spellcasters are literally playing an entirely different game from those who are not. Magic dominates the game, right from 1st level—by 21st level, it’s simply not plausible to play a non-spellcaster. Spells just do too much.
Which is to say, the epic rules aren’t balanced. This shouldn’t be a shock to anyone—D&D 3.5e doesn’t even make it to 20th in the first place. A lot of players feel it doesn’t even handle 7th acceptably, and it’s really genuinely difficult to maintain a cohesive game in the face of the absurd power of 7th-, 8th-, and 9th-level spells, even when everyone is trying hard to play nice. Once you move past that, there’s almost no hope, and I cannot more strongly recommend against trying to use the epic rules for any purpose.
Anyway, if you really want to wield a larger weapon, get a pair of strongarm bracers. They’re still not very good—increasing weapon size just doesn’t accomplish very much—but they’re reasonably cheap by mid levels, and they’re about as good as Monkey Grip and Wield Oversize Weapon combined. Or just become larger yourself—stuff like expansion and righteous might are legitimately quite strong, and being a goliath and grabbing mountain rage isn’t bad either. But that’s because being larger is ever so much better than simply having a bigger weapon—primarily because you get the reach.
It doesn’t, and there simply is no good reason the quoted description should claim it does. If you were fighting with two weapons while also using one or more natural attacks, you could use Two-Weapon Fighting to reduce the penalties on the two weapons when you use the two-weapon fighting option, but it wouldn’t do anything at all for the −5 penalty on secondary natural weapons. So far as I know, Multiattack is the only¹ feat that touches on that penalty, reducing it to −2. Since in this scenario you already used your primary hand and offhand for your weapon attacks, you can’t be using them for your natural attacks—you must be biting or something. And that being the case, those natural attacks don’t take any penalties from the fact that you’re using two-weapon fighting, which explicitly applies penalties to your primary attack and offhand attack. A bite or similar isn’t either of those and takes no penalty.
However, Paizo has, at times, demonstrated extreme confusion over their own² two-weapon fighting rules. Cf. the whole “flurry of blows is two-weapon fighting” fiasco, which still doesn’t make any kind of sense. This description of natural attacks is not found in D&D 3.5e, so it’s new Paizo text, but the two-weapon fighting rules are from D&D 3.5e, so it’s Paizo text referencing Wizards of the Coast text—incorrectly. Wizards of the Coast wrote a lot about how two-weapon fighting,³ and we know that they had absolutely nothing to do with natural attacks.
The only scenario in which I can imagine that Two-Weapon Fighting would directly improve one’s attack bonus with a natural attack is if you attack with a one-handed weapon, and using two-weapon fighting, attack with an “offhand” weapon that doesn’t actually use your hand, like armor spikes. Then, arguably, you might still be able to use a claw on the hand that didn’t use the one-handed weapon, and that might be considered offhand in that scenario and thus subject to the offhand attack penalty from two-weapon fighting, which the Two-Weapon Fighting feat directly improves. Problems with this abound, however: Paizo has stated that armor spikes still (somehow) use your hand, so getting to make that claw attack at all is dubious. And if that is allowed (which it would be under the actual rules they wrote, ignoring the FAQ), then IMO that is the offhand attack, and the claw isn’t. I have my doubts that this convoluted, dubious scenario is what Paizo had in mind when they wrote the description quoted in the question.
D&D 3.5e has an Improved Multiattack feat in Savage Species, which eliminates the penalty altogether, but there doesn’t seem to be a Pathfinder analogue. Honestly, Improved Multiattack was, for most characters, not worthwhile. Multiattack is a very good feat for natural-attack-based characters in both games.
Note that the two-weapon fighting rules are copied verbatim from D&D 3.5e, so it seems their problem here is misunderstanding those rules, and then not being willing to admit that after the fact.
For instance, “Rules of the Game: Two-Handed Fighting,” Part Two and Part Three, and “Rules of the Game: Unarmed Strikes,” Part Two. And, to be fair to Paizo, Wizards wrote all this because those rules are confusing—but Paizo had their chance to rewrite them when they wrote the Core Rulebook and they didn’t, so pretending after the fact that they did rewrite those rules—or that Wizards of the Coast had written something other than what they had—is nonsense.
Best Answer
The Epic version is 3.0 material from the Epic Level Handbook, which is overruled by 3.5 material such as the other version, which is from Player's Handbook II.