The 38-55 has a slightly larger case, 10 gr more case capacity so you have the option of about 2 1/2 % more velocity with the same bullet weight all other things being equal AND a much bigger bullet diameter and potential of almost twice the bullet weight.
All this translates into a more effective kill delivery system..."all things being equal". The only way to know for sure is to load each to their optimum potentials and go hunting...objectively.
I would much rather use my 356 Win levergun than a 30-30 levergun, and I think the 375 Win is even better... except if I used my 45-70...then again there's the 510 Makatak...
...ah-ha...the picture is forming...the bigger the better....hahahahahahaha
At the lower velocities you are shooting, the larger, heavier bullet would still be more effective I think, but it depends on what you are shooting at and how far away.
I've taken several nice elk and deer with a 54 cal LYMAN Great Plains smoke pole shooting a 0.535" round ball with 80 gr Goex FFG at around 1575 fs. Most just folded up, a couple took a few steps, but all the animals were within 30-75 yds and all the balls penetrated through and through. BIG holes. That load is just about equal to the load you are shooting.
As usual...answers contain a lot of "it depends"...and so it does.
The 38-55 and the 375 Win are equals for all intents and purposes and the 375 Win, in rifle AND pistol form has taken game all over the world...BUT..."it depends" on all manor of factors.
Luck