I have been dabbling a bit with equalizers, but what programs should I use in order to make the music better sounding?
There has been on YouTube for example of a Remaster of Belphegor's "Necrodaemon Terrorsathan" album and it sounded better than the older upload. It wasn't re-recorded.
I am not talking about processing the music before it is mixed and mastered, but using a song that has already been studio-released to improve upon it.

Remastering is a matter of EQs, compression, limiting, maybe stereo image enhancement (if it's wished), and maybe some process through tape (analog or just simulation).
Besides (although I have not listened what you are mentioning above), standards from the past are different from standards of today; it means that dynamic range, and so on, the "air gap" between the highest signal peak and the 0 limit, are different now than yesterdays; that's why in the past, the albums used to sound a littler lighter in volume (it means to be more "tape-fidelity" in sound), as today it all sounds louder, pristine, clearer, and with less dynamic in the final result (everything is crushed the f&%k up); this is the main reason about so many people wishing old sound vinyls, tapes, and let the digital era technologies aside.

All that said, there are (for us, simple mortals) plugins that recreate old analog mastering consoles, that allow you to reshape the sound of an old mix.
Waves, IK Multimedia, Slate Digital, are a few options for you if you want to dig it deeper (Slate my one and favourite choice all the way)