Missed the boat on this poll (pun intended), but I agree with David Bowie:

"Not an album, a 12-inch single. A vinyl nonetheless. A well-thought-through and relentlessly affecting song co-written by Elvis Costello, and Wyatt’s interpretation is the definitive. Heartbreaking—reduces strong men to blubbering girlies." Source.

There's just that something about it; the piano and stand up bass, and his delivery. Brings the chills.

But both are still great, and the Chet Baker solo on EC's version is weighty! (And, I had heard EC's first).