Perhaps one of the main reasons I am so happy with the Genesis Collection on my PS3 is because I got it for dirt cheap in a clearance sale. New, packaged and in mint condition. Yet, the sheer fun I've gotten from that little disc has been enormous.
I also did notice a very slight difference in the overworld theme, but the rest of the music is the same as I remember from the Genesis.
I seem to remember PS4 having some special characteristics in its programming that more or less would equate it to Shenmue 2 on the DC in terms of complexity. That is, however, something I read somewhere, a long time ago and should not be taken seriously. Still, if someone knows something, do tell.