You know why, It's stellar original score aside some times licensed music can make all the difference.
[I will never forgive the existence of the third game. It's irredeemably bad and I hope the writers are all damned to Hell]
Did the third game at least have a decent soundtrack? It was done by Paul Ruskay as well and I can't imagine that he fumbled the ball as hard as the rest of the team.
As for my answer, the Silent Hill series. Akira Yamaoka came out swinging with the soundtrack to the first game, it ended up being a four hit combo and even when he did the soundtrack for the less impressive games, it was still part of the series's DNA, though I always felt like he wasn't quite as into those soundtracks as 1-4. Still some great tracks to be found though. I thought Daniel Licht did well enough for Downpour too, RIP man.
I feel the Twisted Metal series always had a bangin' soundtrack, even when the series was not at it's best. It had lots of great original tracks and there was a ton of great licensed music too. The best would have to be the menu theme for Twisted Metal: Black. It captures the mood of the game perfectly and only enhances the car selection screens further. Whoever came up with those deserved a big bonus because they are fucking apex peak uber super duper menu designs.
The Devil May Cry series also comes to mind. From the rockin' battle tracks to the sometimes weird ambience outside of battles, they've always set the mood perfectly. I don't have much else to say, they just wouldn't feel the same with different music.
Finally, the F-Zero games, especially GX. I will never shut up about the F-Zero GX soundtrack, you'll have to pry the hard drive they're saved on from my cold, dead hands.