I'm sure mstat appreciates all the off topic advice, lol.
To your point, both the F250 and 350 4x4s are about the same height off the ground.
Who,ever posted that the 2015 F250 sits higher than prev years, incorrect. Got a '15 250 sitting in my drive that is Identical to the '13 250 I had last year. Both 4x gassers. Unless the 250 you're referring to has a heavy camper package or something, std 250s have 3 rear leafs and minimal blocks. They are lower in the @ss end than both GM and Ram.
A 250 will handle your trailer fine. But not knowing what year you have currently comparing to, I can say the payload of the new 250s is pretty anemic. Needs another leaf.
Getting a work truck version with 17"rims and small tires will help. Will gain you about 1.5" in lowered ride ht over the 20s with big tires.
Get some good nerf bars, drop steps or Amp retractables. Fords have grab handles both sides in the cab.