Do you *feel any difference?

a very tiny bit. relentless is a tad more harsh.

but barely.

Both are polysyllabic, with different stresses - so it's an ideal case for adapting the choice of the word to the melody of the sentence..

I would say that "unrelenting" seems slightly more active, purposeful, willful, or something like that.

The relentless pounding of the waves on the beach wore away the sand.

Those damned waves are unrelenting! Why won't they stop?!