I mostly just applying my undergrad chemistry classes here to make an educated guess, nothing official...

Reactions are limited by the quantity of reagents and the mixing rate. As reagents are consumed (or produced), fresh reagent must move towards (or away) from the active anode and cathode for the reaction to continue.

In flooded liquid electrolyte batteries (like lead acid), mixing is very high and it's surface area that affects charge/discharge performance. In absorbed mat chemistries like most modern lithium ions, surface area is very high but electrolyte is "trapped" next to its immediate cathode/anode and cannot easily migrate throughout the matrix.

In lead acids this sort of diffusion is extremely fast. In packed lithium ions it is definitely slower. When diffusion is too slow, the lithium ions will form dendrites (little spikes) where a gradient of ions exist because they are being deposited onto the electrode faster than the electrolyte can move ions. Thats usually what kills batteries over time and why ultra fast charge/discharge cycles are terrible for them.