It works pretty great. I have my iPod synced to a BT speaker and use that in place of a stereo. Compared to the Android version, the iOS Cloud Player takes a fraction of a second longer to open initially. It isn't really problematic, just noticeable. I don't have a huge library so I keep everything store on the iPod. Amazon has done a fairly good job of matching CDs/iTunes albums to cover art that it doesn't have in its library.
The iOS version seems to do a better job of matching the music together though. For some reason on my Android apps, my copy of Don't Look Back by Boston is broken into two separate CDs (? there is only one 8 track CD for this album?) but it doesn't do that on iOS. A couple of my Christmas CDs have weird breaks (extra CDs etc that aren't on the actual album) but I'll excuse that for being obscure Christmas albums.
Not to sure about how Amazon figures my music should be broken into genre. I have Foreigner's discography but the only "classic rock" album is Mr. Moonlight, and the rest of it is mixed between "Rock" and "Pop"
Sound quality is great though.
Cloud player is screwy with track listings I have. Albums I have some are split into a bunch of different albums because the artists weren't all the same on the album or I have the track numbers out of order.