What constitutes "good music" is subjective, much like beauty. Ergo, there is no point in saying whether or not Starcraft I's soundtrack is better or worse than Starcraft II's soundtrack -- it will vary on a person-by-person basis.
That said, it IS possible to assess and compare the technical and thematic qualities of music. Please bear in mind that I'm not a music authority; I know what I want to say, but I don't know how to say it. Please feel free to correct me.
In Starcraft I, the Terran music blended the banjo with the electric guitar and other more conventional instruments. This created a kind of "metal-instrumental-western" effect. Starcraft II continues this blend with the Terran soundtrack, with significantly increased production values (more instruments, more variation, higher sample quality, etc.). Personally, I was really impressed with the Terran soundtrack in both games, and enjoyed them both immensely.
The Zerg, meanwhile, were characterized by a heavily synthesized techno style, supplemented by stock sound effects. Though Starcraft II continues this trend, the Zerg music in Starcraft II is much less thematically unified than the Starcraft I Zerg music. The myriad Zerg tracks in Starcraft II are not organized around any particular emotional theme. Rather, they appear to be more of a generic assortment of riffs and tones, thrown together with some semblence of organization on a track-by-track basis, without a consistent emotional invocation.
The Protoss see the greatest difference between Starcraft I and Starcraft II. In Starcraft I, the Protoss music was characterized almost entirely by classical instruments and synthesized vocals, and each track had its own internal thematic and narrative arc.
In Starcraft II, however, the Protoss music is little more than sonic wallpaper, quasi-instrumental tones cut together with minimal variation, thematic content, or emotional invocation.
Edited by Unrepentant on 2/10/2013 3:03 PM PST