I don't know the Cuban sound well enough to know the accuracy of Pacino's accent. But in terms of sheer heavy-ness of it, IMO it's not bad.
There's a phenomenon with familiar actors where even a little accent goes a long way in our minds. Look at Nic Cage in "Con Air" - the accent seemed really heavy & bad & overdone. But it's not really inaccurate for the character, it's just farther-out than we want to hear from our movie stars. I have met some deep rural southern guys whos accents really do sound as "overdone" as Cage's accent in that movie.
Here's the thing, though. Doing an extreme accent requires both skill on the actor's part, and the ability to accurately get across the regionality of the accent. Like, Natalie Portman's "British" accent is ATROCIOUS because it's not really "from" anywhere. It doesn't track to an RP accent, it doesn't track to any region, let alone any sub-region (e.g. "the sorth" vs. "estuarial" vs. "East London"). It's just "here's what an American thinks British people kinda sound like." To be fair, a lot of English actors do the same thing when they do the "hard-R generic American" accent. Very few actually manage to pull off a convincing American accent, let alone a regionalized one.
But if you're gonna do it, ****ing do it right, ya know? If you're going to try to take on a Southern accent, root it somewhere. Alabama, Georgia, Mississippi, Kentucky, these places don't sound alike, and they can get even more particular depending on where in the given state you go.
All that said, you do have a point. Cage's accent might actually be from some parish in Louisiana (other than New Orleans). But you don't believe that it's supposed to be, because it's just some doofy "big 'splosions" action flick that you're not really taking seriously, so why would Cage take his accent all that seriously? Like, he's not gonna hire a dialect coach to help him nail a De Soto parish accent in a movie like this.
With Pacino, though, he's playing a serious (if over-the-top) role, so you'd figure he'd try to take his accent seriously. And the whole thing just comes across as...ridiculous. I mean, the rest of the film is decent enough that you can get lost in the story, but Pacino's accent just yanks me right out of every scene, as do the accents of Robert Logia, and Mary Elizabeth My Hair Is Crazy In This Film.