Okay, so I've now listened to both Imogen Heap albums in their entirety, and now it's a little easier to see the difference. Different instruments and styles are indeed used to achieve the emotional effect desired... I just don't really have the words to explain it. The solo albums are more intense, and use more of an Alanis Morrissette set of instruments: guitars, synthesizers, and the like. The beats on the solo albums are a bit more complex and jarring, and the background music is a little pop-normal, with less of the ethereal quality that the Frou Frou tracks have. The Frou Frou CD has an Amélie cuteness that the solo albums don't.
Imogen Heap's second solo album, Speak for Yourself, is more like Frou Frou - Details than her first album, I Megaphone. Out of the three, I like Details the best, then Speak for Yourself, and then I Megaphone, but they're all very good.
Those of you who enjoyed Frou Frou's album—and I know there are quite a few of you—should check out Speak for Yourself. (I'm done talking about Imogen Heap now; time to find something else to write about.)