I know their are a lot of folks on this site that know a lot more about trucks than I do but as you say, I think it is just the additional suspension. I went with the 350 for this reason as I plan to purchase a truck camper in the near future.
I was raised on a large ranch as a kid and we too had gooseneck horse trailers which we used 350's to pull. Thats not to say the 250 couldnt do just as well.