The Monkey Grip feat enables you to wield a larger weapon at the cost of -2 to attack.
In the best case, a larger weapon gives you 3.5 extra damage: Greatsword 2d6 -> large Greatsword 3d6. The increase is even lower for smaller weapons.
Power Attack gives you more damage increase for -2 to attack, and it is more flexible, as you can change your attack penalty and damage benefit from round to round.
Why would I ever pick Monkey Grip?
Not only is it a net negative to use it, there are myriad options that can do the same thing better, for less cost.
Strongarm bracers, 6,000-gp arms-slot magic item from Magic Item Compendium. Lets you wield larger weapons at zero penalty, and 6,000 gp is worth a whole lot less than a feat. It explicitly does not stack with powerful build, and does not stack with Monkey Grip thanks to the particular wording.
Powerful build, found on these creatures. Count in many ways as a size category larger, including wielding larger weapons at no penalty. There is no way to get this benefit without at least LA +1, which is a higher cost than a feat, but it also comes with a number of other benefits.
Fullblades are an exotic weapon from Arms & Equipment Guide, a 3.0e source. The changes in how weapon sizes were handled between 3.0e and 3.5e are significant, and that leads to a lot of groups just deciding the fullblade is a Large bastard sword and being done with it. That said, A&EG statted it as an exotic weapon for Medium characters (with extra-special rules for Large characters), so if you maintain that, Exotic Weapon Proficiency in a fullblade would get you the damage of a Large weapon without any penalty for using a Large weapon (because you aren’t, you’re using a Medium weapon). Exotic Weapon Proficiency (fullblade) is still a bad choice for your feat, but it’s a whole lot better than Monkey Grip.
Just fluff it. The descriptions of the weapons are all intentionally vague to allow you to describe your character the way you like. There is no reason at all that your greatsword cannot be described as Cloud’s buster sword or the like. Your character’s appearance, including the appearance of their equipment, is largely up to you and you should never have to spend a feat on it.
Monkey Grip might not be the most optimal feat for improving damage output. However, if your goal is to make a giant sword wielding bad*ss - it's a great way to make your character sound cooler.
From the perspective of optimization, the damage step-up between weapon sizes gets larger the larger the weapon category. For example: a colossal greatsword (8d6) is 2d6 more than the gargantuan greatsword (6d6). So, if no other better optimization is available, giant characters see a higher return on investment for the Monkey Grip feat.
Power attack is limited by your base attack bonus.
Should you happen to be in that part of the game where you hit very often despite full power attacking, losing some more tiny amount of precision to get that few more damare might be advantageous.
Of course you might be wearing Strongarm Bracers instead, but maybe you want those other bracers and your DM uses the pretty common houserule of not letting you combine multiple magic items into one.
(Of course, KRyan is also right. There are a ton of other better feats out there.)
Because you can still stack Monkey's Grip, expansion, powerful build of a half-giant, and Power Attack. This means a half-giant of 6th level can hit like a bus just by spending one level in psychic warrior to manifest expansion and five into barbarian. Easier still, one psychic warrior, two rogue means you can be hitting neat 6d6+ with a greatsword at level 3. Yeah, LA is somewhat a problem, but it's simply too much damage.
Then you can keep barbarian or rogue side, depending on what you want. People often forget that you don't need stealth to get sneak attack, just flanking or negating Dex by other means, like being on the ground because some psionic stomp hit them.
Yeah, half-giant is a savage build.
