I’m not sure about current prices, but when I bought my F250 price was close enough to the F150 that it was a wash. The Tundra back then actually priced out higher than my F250.
The 3/4t trucks have larger brakes and full floating axles attached to heavier frames. This will result in poorer economy when empty but better towing performance.
Instead of focusing on short or long bed, look at wheelbase. A longer wheelbase will tow straight better but be less maneuverable due to larger turning radius. My extended cab short bed was easy to drive around empty but they shorted me in fuel tank capacity. I never felt I needed a longer truck towing a high profile toy hauler and my combined length was 45’ which made it easy to access tight spots.