What you describe as latin/spanish music (at least traditionally) is firmly rooted in arabic music. Flamenco makes heavy use of the harmonic minor scale and the phrygian dominant mode, which is also the mode most frequently associated with arabic music. This isn't a coincidence, the muslim people stayed in Spain 'til the XV or XVI century, if I'm not mistaken. The cultural heritage is much more noticed in Spain than in Portugal, because we kicked them out much earlier. Portuguese music isn't as firmly rooted in arabic modes, but it's still influenced.
I personally love Lopez's playing a lot more than Axe's. It has nothing to do with the tightness of the parts played, which I admit Axe holds the upper hand, but rather with the feel the player demonstrates. Axe might be a pretty talented drummer, and he must be very dedicated to his practice. I don't feel Lopez is as tight because he doesn't practice as much. My guess is that what he plays in the studio is partly improvised but has a strong theoric background. The polyrhythms on the last part of Deliverance are theoretically very creative, and he certainly had to practice that many, many times. He would have to had spent some time actually training his muscle memory with that pattern, plus some more time actually putting the part to tape. But a lot of the things he plays are just based purely on feel, with no strong theoric consistency, those are the parts he improvises. Those parts he only practices as he records, and even if it takes many takes to get a part recorded correctly, he still won't have his muscle memory as trained.
And that leads us to the live situation. Since many of the parts were not thoroughtly practiced, but only "played", they don't come out exactly as they played on the record, while stuff he has to practice, come out clean and perfect. Often improvisation depends on the mood of the player. This leads to both unpredictable live performances and to strange moments. One watching the concert might think he has been pretty off all night, but then he breaks out one of the tricky practised parts which makes your jaw drop to the floor. Then again, someone watching him on an "on" night, would get the impression that he is an outstanding drummer.
Axe, on the other hand, had to learn every single one of Lopez's parts by the actual parts he played on the records, which in live performances reflects as him being a lot tighter, and at the same time a lot less spontaneous.
