I've been battling with what Media Player to use on Android (too bad iTunes is out of the equation). I've tried Winamp and DoubleTwist -- overall Winamp wins. Winamp is faster, has more features, and more mature. Importing my iTunes library was a breeze. I only had one problem, some files won't sync properly. I found out that to fix this issue is simple but requires some manual work. It has something to do with the files' meta info; either it has no meta info, it has blank values, or it has inconsistent values (ID3v1 and ID3v2).
Simplest way to fix it is use auto tag. On Winamp, select files you want to fix -> right click -> send to -> Auto-Tag. Wait for all items to be queried (click Check All or manually check each file if the status is 'Unsure'). Then click 'Apply Changes' to update the track info for the selected files.
Another way to fix meta info is check if ID3V1 or ID3V2 is more updated. For example if ID3v2 is more updated on a file, right click -> View file info -> ID3v2 (tab) -> click 'Copy to ID3v1'. This should make the meta info consistent.