I've been using Winamp for too long. I've read that programs like JRiver, Avarra, Audirvana should increase the listening experience.

Any recommendations?

You can't get better sound quality out of software like that. Those programs might make the 'media library' experience better he quality of the music itself isn't going to change.

I thought that some apps (on Android at least) use their own sound drivers, which gives them different sound quality ("better" being subjective).

As for the media library experience, I used JRiver for a long time and really liked it, I just found the price for version upgrades too expensive. So I've been using MusicBee instead for the past several years and am happy with it as well. It does take a little while to get a handle on all the customization and other features though.

I've been using foobar2000 for many years. When compared to WinAmp, it just looks better. When compared to Windows Media Player, it actually does sound better. (Recommend not using EQ. Sounds better with EQ off.)

I use MPC-HC for pretty much everything.