If the current is a bit strong for the battery, its deleterious effect uses to worsen with pulsed current.
The simplest difference is heating. If you imagine the battery as a voltage source and a linear resistor (that's oversimplified) then 0A/10A dissipate more than permanent 5A.
Then, you have all non-uniform effects like the creation of spikes. They depend fundamentally on he current density. But these effects tend to harm batteries during charging rather than during the discharge.
A battery may also produce gases (more often during the charge), and if the cycles are slow enough, they can make the difference between boom and no boom. Or the battery may need air, and if the cycle peak exceeds the available air throughput, everything changes.
And so on and so forth. This question should not be answered in the general case. Datasheets of a particular battery are the good answer.