I'm not sure about Ram and GM, but with Ford the SRW 350 is identical to the 250. The only possible difference is a single upper overload spring and a taller rear spacer block under the suspension. Both of these items can be had on a 250 as well based on packages ordered. They can also both be added after the fact for cheap money. With Ford, the 250 is de-rated on paper to fill a different market segment is physically the same truck. That said, the two will ride identically...
When buying new and ordering I would and did go 350 as the price difference is less than 800 and someday states may start checking private rigs for weight. If I was buying off the lot and found the perfect deal on a 250, I wouldn't hesitate to grab it though.
As to ride, I would say either Ram 2500 with it's full air suspension option, the Ram 3500 with it's rear suspension, or any GM product with IFS will ride better than a Ford SD. I'm hoping Ford comes out with some ride enhancement in the 2017 re-design without sacrificing strength.