For a battery grip that uses AA cells, the usual tradeoff is cost vs. performance.

• Best performance: disposable lithium AA batteries (such as Energizer Lithium). They generally have higher capacity than regular AAs, maintain performance better as they drain, and are lighter.
• Best long-term value: low-self-discharge NiMH rechargeables, such as Eneloop-type batteries. These are a popular choice for camera gear and flashes because they recharge well and hold charge better in storage than older rechargeables.

Compared with the camera maker’s dedicated lithium-ion packs, AA batteries in grips often provide less runtime overall, even if they enable a higher frame rate. But AAs are convenient because replacements are easy to find almost anywhere.

So, if you want the best all-around rechargeable option, go with quality NiMH low-self-discharge AAs. If you want maximum runtime and convenience for travel or emergencies, use disposable lithium AAs.