I am sorry to say this but I have to agree. Groove sucks.
It doesn't sync my music (for two weeks now, still the same songs on my playlists when I update weekly), it's unable to play some of my music (not sure why since the Hub Tile plays them flawlessly) and it has no customization or whatsoever.
I was satisfied with the Music+Videos app Windows 8 had before but now and ever since 8.1, the music player on WP has been a disappointment which is a bummer since that's the most important part of a phone for me.
Don't get me wrong Windows 10 Preview on my 1520 is GREAT. Everything about the UI, animations and feature are fantastic. The new Weather and News apps my goodness they are literally flawless but then there's Groove. A big disappointment. My upgrade is up since February and if Microsoft doesn't fix Groove until the launch of the iPhone 6S, I will go back to iOS. The rest of the OS is great but the music functionality is the most lackluster among the three major mobile OSes (I mean Android has multiple stock music players that are horrid as well but at least we have options, the options in WP are just as bad as Groove).
Microsoft, please fix this. I've been very active in W8.1 and W10 preview for phones regarding this matter in the feedback, please read suggestions because the app (Xbox Music and Groove) is truly horrible. I think waiting for almost 2 years for Microsoft to fix the app is more than enough.