People ask me what rifle should I bring out west for an Elk hunt? My answer is, what rifle do you use on game back home, Bring it, if you are use to shooting that rifle then you will not have to learn to flinch on a bigger rifle."Big monster trophy bull elk" as you have described would make me consider a cartridge heavier than either of your choices but that's just me. I'd be looking at any of the various 300mags.
.243? Bring it, .30-30? Bring it, .257Roberts? Bring it. Just shoot with in your sure hit range with the caliber being used. Hunting Elk with a .30-30 or .243 is common where I live and accounts for a lot of filled Elk and Moose tags every year!