None of the available apps - not Songbird, not Winamp, nor any of the others - in my opinion are even as good as iTunes, much less better. You can try those out for yourself and see if they suit you, but in my opinion iTunes is still the best, even with the somewhat unexplainable feature removals (notably the ability to open playlists and the iTunes Store in separate windows) in iTunes 11. Showing the sidebard and status bar, as SJF suggested, seems to fix a lot of the complaints from those who just can't adapt to the new layout, so if you haven't tried that, give if a go.
Otherwise, there just isn't any really good alternative that I've found, though perhaps Songbird or Winamp will work for you. If you just want music, you can also try Swinsian:
Yes, I've become a total grouch when it comes it iTunes
Thanks for the suggestions, I forgot about Songbird. I'll give that a look.
I as well, when last checked a few years ago, thought nothing for the Mac was as good as iTunes for music (which is kind of really pathetic when you think about it).
If I find some brilliant iTunes music replacement -- I'll post it here.