I really enjoy a subtle mix of the two flavors in question here.... that is, I really don't like it when all characters have equal potential application in battle.... but by the same token I hate it even more when static potential of characters make them almost completely necessary, or at the very least an obviously superior choice to your favorite gambler with a lousy freakin' "slot" speciality (hehe, I ALWAYS had setzer relic-ed out to be atma-equipped personally.... he was just too cool not to.....)..... as such I found FF6's system, while highly flawed, still great because despite the fact that one of my favorite characters had one of the worst job exclusive skills there was, with the right equipment and some quality time spent with a few select espers he kicked ass... PLUS HE STILL HAD HIS LOUSY SKILL AND JOB which kept him totally in character and unique.... In other words he remained a gamble, just a bad ass gambler whose prowess with a sword was 2nd only to Cyans for me..... This is an example of a good system..... IMO
Another great system was sported in suikoden. True Runes, combo attacks and positioning stengths made each character feel unique enough in battle to be themselves and coax me into their use... while even if I really dug a character who logically was a weaker link, typically switching up runes (if possible), keeping their equipment capped, and sometimes including someone whose use allowed me to exploit a killer combo attack made them completely worthwhile. Naturally there were quite a few characters who were lost causes in suikoden... but come on, out of a 108 characters of course your gonna have some that are unbalanced to an unreasonable extent.....
I typically run into the problem of not feeling as though characters are unique when the complexity of customizing things gets so great, any unique character potential is really an afterthought... this happens more so with SRPGs than anything else for me.... For as much as I loved Growlanser HoW this was a prime example of that flaw.... Placing those skill and growth plates made it so, while stat potential may have varied character to character, there was really NO reason you couldn't simply choose from the lot of em and cast em as any roles you saw fit with little to no reason to select them other than whether you liked em or not.
Then again, sometimes I really just dig the straightforward progression of linear skill sets and spells such as with Lunar. Lunar (well at least the original Lunars.....) battles proved tough enough where they never felt redundant or under-demanding of my cognitive faculties despite the fact that no real strategy at all went into character growth. I like this for the reason the OP made the thread.... Jessica will always in my eyes be a odd-ball healer, because no matter what, she is in fact a healer and priestess even though you get the impression she could be wild enough to equip a pair of gauntlets and beat the piss out of kyle for being a jerk. Now if I had the freedom to in fact equip jessica with said gauntlets, boost her attack whilst neglected her given affinity for the healing arts and have a "warrior priestess-type" she would lose alot of what makes her personally so unique and memorable in my eyes.
Great observation by the original OP about how the application of characters in regard to gameplay does, in fact, impact how fleshed out, complete and memorable a character proves to be.