It's definitely the medium.
Radio, CD, MP3, vinyl, web, and pretty much every distribution method each gets a different master if it's in the budget.
I disagree. Unless you're one of those people who magically hears liquid gold earsex from vinyl (which is more a psychological thing and is pretty much proven to be BS), the real difference isn't the medium, its the version of the recording. The problem is you've been listening to modern produced music (even if its old, you're likely hearing "remastered" versions if you've been listening to AAC versions).
I'm assuming this is an old record, or maybe a repressing of an old record master as its source? The difference you're hearing isn't about it being vinyl but about it coming from an era when production/mastering didn't ruin shit for the sake of it.
From what I've gathered that's not true these days. Vinyl might and maybe if its a special mastered version (like on HDTracks or Linn Music), which sometimes is actually a completely different recording, but now they put almost the same shit everywhere (it might be different format but you're just deluding yourself if you think there's a drastically different mixing that would make up for all the shit they'd already done to ruin it). Radio, download, and CD are all coming from the same shitty produced source these days. They might tweak it some (they claim that for the "Mastered for iTunes" or whatever BS them and Apple tried to come up with, but those don't actually sound better). Things can sound different on radio because its being broadcast analog (unless its a digital form), and if you're lucky it might still be coming from an analog source but most radio stations are just streaming a digital file from a computer/server.
Even comparing the mastering differences, your speakers still have every bit as large an impact on the sound you get.
Also, don't be one of those fucking idiots that goes home to a quiet suburban house and just focuses on listening to music while you're drunk/high and then complains how it sounds so much better than you listening to your iPod/phone and $20 earbuds while you're on the train, or walking a down a busy street, like the only difference is the fact one is MP3 and the other is vinyl.