Your kangertech toptank mini is 22mm, which will fit most, if not all devices. Your presa is a built in battery mod and you need to decide whether you want to continue with built in type or "stepping up" to an external battery mod. With an external you'll need a charger and spare battery. The advantage is you don't toss the mod when the battery dies.
I don't think I would characterize external batteries as a step up from a LiPo. Both have their pros and cons. Li Po's can have high mah- cdr's in a compact space (think true DNA200) and have a longer life than many 18xxx 20xxx batteries. As has been stated "mAh and Amp capabilities dictates Battery usage time. Battery life is dictated by use and abuse."