Mark Clark's observations make sense--changing the key for a given piece often necessitates corollary changes in instrumentation, vocal assignments, etc., all of which obviously will affect the nature of what we hear.

I will still contend that if NOTHING else changes except the key, the music will sound essentially the same. Now, there may be a few people for whom this is not true, including apparently Barbara Shaw, but I would think the overwhelming majority (excluding those with perfect pitch) would not detect any difference, much less a significant difference, between a piece done in D and the same piece done in Eb, if there are no corollary changes.

From my personal experience, there are a number of songs that I have performed in different keys without sensing a difference in essence or character (nor has anyone listening mentioned noticing such). Likewise there are quite a few I have heard in different keys, and I find the song and its presentation are central to the feel, but the particular key seems to be immaterial.

Modulations are indeed interesting. Again, I find their significance to be in the existence of and magnitude of the change, not which particular keys are involved.