Not a matter of how much cache you have. SMR are good for storage archiving. When you write once to disk and there's not many read/write which is what heppens for a day to day PC/system/console. The SMR drives have slow read/write speeds compared to CMR which won't cause much trouble for running PS2 games I guess. Bandwidth would be enough but I won't use a SMR drive for this purpose.
Does the PS2 drive bay support/accep SATA drives? I think back in the day the Sony HDD and network support to fat PS2s they used IDE hard disks on the console. You might need an aftermarket adapter of some sort I reckon. You might already have this I guess?
TL;DR: I'd get the CMR drive.