Not sure what you're using to get that much velocity out of the little 250, but my 22" Ruger only goes about 2825 with 35 gr H4895. The highest I've seen listed with a 24" barrel is just over 2900 with H4895 or CFE223. Not saying it's not possible, just that I've not seen published data that shows that much out of a 250.
I routinely run 3050 with 100s in my Ruger 257 Roberts with below max loads.
There is a velocity advantage to the larger case in a modern bolt action, but I'm not sure too many deer will be able to tell the difference.