I'm going to hedge a little. If put to the test scientifically, I would probably fail to identify nuances between a song in D versus Eb. However, if tested, I'm convinced I could feel differences between Eb and G, for example, a wider range.

Here's something I actually did: I used to play the Chopin Nocturne in Eb on the piano. It is a dreamy, moody, melancholy piece. I transposed it to G for the guitar, and then cleverly renamed it Chopin Nocturne in Eb in G. Now it's a rolling, cheerful thing with sweet spots that were not apparent in Eb. Much of this is because of piano vs guitar. Some because of my limitations on the instruments and how I interpret it on each. But some of it is because of Eb vs G. No doubt about it. Try it!

Some of the differences in "feel" on the same instrument can be attributed to the difference in physical experience playing in one key vs another. Playing a piece on the piano in Eb is very different from playing it in C. How you hold your hands, how you lean, whatever. Never having taken any theory courses, I can only offer subjective opinions and impressions.