Just to present my own experience: I recently sit in an algebraic topology class, the main subjects are fundamental group & covering space, and homology theory. For the fundamental group & covering space part, I feel many textbooks exposit them well(e.g. John Lee); while for the homology theory part, our recommended textbook was Allan Hatcher's renowned textbook, but I find it very hard to follow, and the long winded paragraphs of informal discussions are sometimes just impossible for me to figure out what the core content is. Later I switched to G.Bredon's GTM textbook Topology and Geometry, I feel it is much easier to follow and the content is no less than Hather's.
But as a word of caution, as you are probably already awared, this is just my personal biased experience, and experience differs from person to person. From some informal statistics I suspect Hatcher's book will win higher votes among math guys, and I think it is probably true that the "long winded paragraphs of informal discussions" in Hatcher contain many gems. The problem with me is that, as a physicist without too much appreciation of abstact mathematics(I tried, but failed to appreciate, and not proud of it), I learn subjects like homology because it is going to be useful, constantly doing things like "diagram chasing" just doesn't entertain me, so when I read I tend to make notes about and sometimes even copy down the theorems and proofs, just to prevent my brain from shutting down. This usually doesn't happen when I read a good physics text, where the content just resonates with me and I can think about and remember it even without writing. So probably for me Bredon's book wins simply because he lists the core theorems/lemmas/corollaries in a much more organized manner.