I wouldn't personally buy a 6.0 or 6.4 Powerstroke. The 6.7 has been better but that limits you to (I think) 2011 or newer.
As far as that era F250/350 goes, you aren't missing anything. They're either identical or identical aside from an overload spring and a different size axle block on the back. If the F250 you find is missing the overload spring, you can fix that by either adding one or installing bags/timbrens, and now you've got the same truck as an F350 (assuming tires are the same - check that too). Chassis, axle, brakes, etc. are all the same between the two. The difference in payload rating boils down to a heavy truck coupled with a class maximum GVWR on the 250, so it's an on-paper distinction. I'd tow that weight Fifth Wheel all day with a 250/2500 class truck as long as the tires were up to it.