I agree that Chrono Cross would have fared better without any prior connection. It feels forced and cheapens things.Going more old school, Chrono Cross was fine, just not a good Chrono Trigger sequel. The 3rd Birthday is a great third-person shooter, but it's not what Parasite Eve fans expected/wanted (and the story is incoherent). Streets of Rage 3 is good, but people wanted more melodic tracks I guess.
PE's sequelitis is a trainwreck. 2 and 3 should have been released as something else, so I wouldn't care for how middling they felt.
I don't think the real problem with SoR3 is the soundtrack, it's more like the difficulty changes from the western version if anything. Yeah the music doesn't hold a candle to Sor1 or 2 but it wasn't bad.