Puerto Rican or the ones that I hear/speak to here, are rarely natives so their Spanish is very anglicized (some of them, to be honest, I may speak better than them), but I distinguish them with their "r" which is harsher in my opinion. For a long time, I could distinguish between Caribbean and others, but couldn't point out which island. Now, it s obvious, although I think Cuban and Dominican sound alike, their "musicality" is very different.
A good friend of mine is mexican and we speak in Spanish, she is easy to understand, but if I overhear mexican workers speaking among themselves can be a bit more challenging as they have their own slang.
Whomever, I speak to, they can tell I learned Spanish speaking with Dominican despite my french accent (but I think it's my choice of words)