The 250 and 350 Tremor (given the same engine choice) are mechanically identical because the 250 requires the high capacity tow package. The only difference is the gross vehicle weight rating (250 diesel: 10,800 lbs, 350 diesel: 11,500 lbs). This difference means an identical configuration of the 350 diesel will have a 700 lb higher payload. Gas units have different GVWRs but I think the difference is the same.
Some states (cough: California) require a higher registration fee and that you stop at weigh stations if you have GVWR of 11,500 lbs or greater. If your state doesn’t have that, then the 350 is pretty much always the better choice just because of potential resale and higher ratings for the same equipment (future proofing).
For 20MY, it was $1000 more for the 350 and (for some reason) you couldn’t select the power deployable running board option on the 350 tremor on the build and price tool. I live in CA and while I could live with the higher registration, I didn’t want to stop at all the weigh stations when I want to road trip... so I have a 250 diesel.
Good luck with your purchase!