The Intro to Algebra (and other course books) feel more structured and systematic. They work their way through large topics on step at a time, and include all the teaching you'd need to understand the material.
We found the AoPS V1&2 a bit more scattershot. They're full of interesting material, but they are the first books Rusczyk wrote, and they can feel like a bit of a brain dump of his lifetime of math contest experience. There's lots of good stuff in the there, but the complexity, level of challenge, and assumed prior knowledge can jump around quite a bit. It can be a fun place to randomly hop in and out of for practice and fun, especially if you are getting the basic teaching elsewhere, and just want more practice/ challenge. They weren't really designed to be a coherent and linear course in the same way all the other books are.
As for verbose - - - well, the Algebra et al does contain a lot more background and explanation, as they tend to start everything from first principles and assume less prior knowledge. We also found them a lot easier to read (far more whitespace, better layout, less dense text and a lot more visual, diagrams, etc - more show, less tell). In comparison, V1&2 are more efficient, but my DS - who is very visual and not so good with words - found them a bit of an unappealing wall of dense text.
The course books worked a lot better for us, because we were using them as our primary and first teaching of the material (not supplementary to stuff he was learning elsewhere). With the Algebra and other course books, we have found the layout makes it really easy to jump over pieces he knows how to do and focus on the ones where he needs more info. While the text does takes up a ton of space in the book, there is not a lot of text that is independent of a specific problem being solved, so it's really easy to see which text you need and which you don't. The format of each chapter tends to be: very brief intro to a concept, example worked through, handful of problems worked through together to explore a bunch of related concepts, then the actual section problems, then the end of section problems, and challenges. Each of these parts looks different (font/ color/ boxes, etc) and are easy to see. So we've found it really easy to navigate when we're going back to concepts he knows, scanning through the sections/ problems to confirm "can do it; can do it; can - whoa, wait a sec, what do you do with that one? Let me think about this a sec...." For us, it's been really easy to hone in on the text we need and gloss over that which we don't.
