ASITA is definitely a great album, and I feel like it feels more upbeat than the two albums surrounding it, which I feel are a bit more dense and thus, possibly harder to get into right away, but that's part of the charm of Andy's music and The Tangent in general. His music seems to go in waves like that.
APITQ was one of my all-time favorite albums when it came out, and I still think it ranks up there. The opening and closing epics are some of my favorite songs of that length, and showcase just how powerful Andy's writing was, even after the departure of Roine Stolt. I think having Jonas Reingold stay with the band for nearly it's whole life so far has been one of the best things about The Tangent - he is their Chris Squire, if you may. That isn't to say Jonathan Barrett's work on DAOIPAL or COMM isn't good, but Jonas' signature bass playing helped define the Tangent sound in it's first few albums.
If you find yourself listening to the first two albums, you'll definitely hear more of the Crimson, and even Van der Graaf Generator influence in there, especially with VdGG's own David Jackson playing sax and flute on the debut album TMTDA. He was replaced by the aforementioned Theo Travis on their sophomore release TWTWDT, and his playing, alongside Jonas, also helped define the Tangent sound.
-Marc.