Mine is Strawberry since it has a ton of options and plays a ton of formats. It's also (distant) fork of Amarok 1.4 and integrates well with KDE Plasma. I'm curious what other people are using these days. What's your favorite player?
For what it’s worth, I have this problem sometimes when an album has multiple releases and you can choose which release to pull tags from via the context menu in Picard. There’s also a pretty powerful scripting language that you can use to specify the directory and file re-naming structure as well. It took me a while to get my structure set up properly but once I did it’s been a life saver in keeping my files organized.
If there’s something in particular you’re trying to achieve that’s not working I’d be happy to try and help!