Either will do the job very well. If I were in your shoes I' d look for the make of rifle you want first then decide between the two for caliber. I was tempted to purchase a 300 WSM but the rifle I wanted (Tikka WH) didn' t come in it. Does come in 7mm RM, and .300 Win. Since I already had all the reloadings for the 7mm I stayed with it.

If you can go shoot both with factory loads. That will let your shoulder do the talking. Either will do fine I think for moose and antelope and even up to a full-grown Elk (with proper bullets and good shot placement). You get a little more energy and frontal energy from the .300 but it might be more gun than you really want to shoot a lot. Best to try both and see which one you like.