Before we begin, it is important to note that the music in StarCraft II is very much not finished. There is only one piece of music for the Protoss, while the Terran and Zerg have 5-6. So naturally, this will change over time.
It is also important to note my general feelings on the music in StarCraft I. To me, it was hit and miss. Most of the Terran music was good, the Protoss music had occasional insight, but the Zerg music was just blah. Except for the Radio Free Zerg song.
As for the StarCraft II music... it is pretty much the same style of music. Indeed, it may be too much of the same, but I'll get to that a bit later.
The SC2 menu piece is very good. It has echoes of the original main menu, but with some of its own character. Although, I have to wonder: why a 7 minute piece for a menu, when the menu for Battle.Net has a different theme? Anyway, the main menu piece seems very much like a StarCraft II Overture. It has echoes of Terran, Zerg, and Protoss themes. The Zerg theme you may have heard in the Zerg reveal video, though here it is done much better. The piece flows into the different movements reasonably well.
The Battle.Net menu music is unintrusive, but not something you're going to actually want to hear.
The in-game music is probably the least changed. Oh, it's recorded with better instruments and sound quality, and they are different compositions. But the style is still very clearly that of StarCraft I.
I would say that the most improved is the Zerg. In SC1, the Zerg music was mostly just noise, devoid of anything resembling a melody or real music. In SC2, they still have some of that quality to it. It uses many of the instrumental sounds of the SC1 Zerg, so it still hearkens back to its roots. Even so, it manages to actually have a point in SC2; the music sounds like something that grows and festers.
The Terran music is probably the least changed, thematically and instrumentally. Indeed, it seems to have somehow become more guitar-y than it was. This leads to certain riffs that sound like they came out of Firefly or something. There are other riffs that are so close to those in SC1 that you'll automatically assume that they will continue directly into one of the Terran pieces. This is not the case.
As previously mentioned, there is only one Protoss piece currently, so it is harder to evaluate it. Even so, it seems similar to the other two: no thematic differences and retaining the same instruments.
There is something missing from these pieces. And that is a definitive statement, a unique signature. See, there is nothing about these pieces that is unique outside from their identity with the original StarCraft music. And that is a problem.
Let me explain by analogy. Take the main-line Mario series of platforming games. Each of them has different music. And while the most iconic is the main level music from Super Mario Bros. 1, there is a clear understanding of what "Mario music" is. The main level music from every Mario game has it, from SMB3's more playful, almost toylike theme to Super Mario 64's energetic directive to seek and find. Each theme has its own identity, but they all have stylistic similarities to one another. Each theme pays homage to what came before, but they also have their own distinctive qualities.
There is none of that here. StarCraft II's battle music has no identity of its own; it is simply a restating of what StarCraft I did. It doesn't even constitute a remix, as that would require putting a different spin on the pieces. SC2's music may have different melodies, but the core of the music is nothing more than StarCraft 1. It has no voice of its own, no soul of its own; it is borrowing the soul of another game.
What the music is saying is that it is music for "StarCraft II", not "StarCraft II."