Biggest physically? Or biggest capacity..
I have the 3.2A Powerbank (in both black and white), both work great. I chose the white color over the black but was careless when assembling and snapped the top of the case. Replaced it with a black which has a really nice soft texture feel to it. Case adds a nice bit of heft to the phone and doesn't reflect or otherwise interfere with the LED flash.
There's a brand new 4.2A Powerbank (black only afaik). I ordered one over the weekend so will probably be sometime next week before it shows up. I'll post more info when I get it.
There's also the Mophie but it doesn't offer enough capacity imo. If I'm going to alter the feel and profile of the phone, I'm going to get max capability out of it. The M has a slightly different shape and color (more of a gunmetal than black) and a little bit more tapered curve, but the Mophie dimensions are the same as the Powerbank, so they take roughly the same amount of pocket and hand space. Wife has it on her One.
There's one more 3.8A case but as I'm not a fan of the flip over cover I never considered it.
PS - The Mophie charges both the phone and the battery at the same time so you don't have to disassemble anything. The only way to charge the phone and the Powerbank at the same time is to separate the 2 and plug into individual chargers. However, the Powerbank will charge both the phone and the battery sequentially so you don't need to disassemble the case unless you really want to. (1. plug phone/case into charger. 2. press the charger button so the battery case starts charging phone. 3. when it finishes charging phone it switches back to 'ac charging'. 4. huzzah; plug it in before bed, it'll be ready when you get up, etc)
PPS - All work fine with USB/Data/etc.