Re: AAA, CMLL, or Lucha Underground: which is the WWE of lucha libre ?
CMLL is the oldest wrestling promotion in the world, the #2 drawing promotion in the world in terms of total attendance yer year behind WWE, and probably the #3 largest promotion in the world overall behind WWE and NJPW. They are similar to WWE in a few ways: they are mostly TVPG and they are very slow to adapt to changes in the business at large. Where they differ is that CMLL is much more focused on quality matches than storytelling. But they're run by very rich, very competent business people. They're much more professional than AAA, and much more stable.
AAA has certain advantages, too. They are much more media-savvy than CMLL, so their shows are easier to find on TV/online/on PPV in most cases. And they tour constantly and sometimes book bigger venues than CMLL. This is because CMLL owns all of the venues they run shows in (about 5 venues in different parts of Mexico, from 2,000-17,000 seats). But financially they've always been a mess, partially because of the licensing and trademark issues mentioned above, and partially because the family that owns them is a bunch of carnies. They split off from CMLL in part because of frustrations about their conservative philosophy with respect to booking and change. Consequently AAA is pretty much willing to try anything. Sometimes it's a good attitude to have but often times (very much so recently) it just ends up looking like a gong show.
AAA is probably the #4 promotion in the world, slotting in just ahead of ROH.
Lucha Underground is great but it's a blip on the radar in comparison. They're not even on the level of an Impact or a Dragon Gate on the global scale.