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The power build, adds much more Ability Power than the other. It is more of a hybrid, as you buy items that add both Ability Power, and Attack Speed. Shurelya's Reverie, is for mana regeneration, as well as to help with you being squishy. This build also has cooldown reduction, and much mana regeneration, as you'll want to spam you ult much more than the other build, and there for want to be able to get many shoots of quickly, while still having plenty of mana, as the ult's mana cost increases. I've done really well with this build, and make Kog'Maw much more dangerous from afar.
Basic builds, that really can make Kog'Maw powerful. Kog'Maw speed is a faster start, and you wanna focus the Bio-Arcane ability, as the attack speed allows you to get many shoots off, and then with Sword of the Divines extra 100 magic damage every fourth hit, you can take down enemies very quickly. IN the speed build, you can replace Rabadon's Deathcap, for a Phantom Dance, but its all about personal preference. I prefer Rabadon's Deathcap. This build is very good, and you can take down almost anyone with this build. Just hit Bio-Arcane and watch their health drop.