Yes, Alexi's solos are like Kirk's old solos, but not THAT much. More like Dave Mustaine's, but with much more melody and, I don't know the word, purpose maybe?
But his old soloing doesn't sound like Randy Rhoads's at all (imo at least). Yngwie is a much more valid person to refer to, probably. Alexi really loved that almost classical style on the older albums. And just because Alexi loves Randy, Zakk, etc's styles doesn't mean he solos like them, you know, cause he doesn't (most of the time).
Here's where opinions stop: Alexi's solos on HCD are the most technical he's ever done. Ask him yourself if you don't believe me. So are Janne's. And yes, he's always had solos similar to Slayer's, once in a while. But to say that his soloing on HCD is like Slayer's, overall, is pretty stupid man. In fact on that album I don't see much Slayer soloing at all. I actually just listened to the whole thing and none of them reminded me of Slayers' style except for maybe the end of the title track's solo. Now if you had said the RIFFS are more like Slayer, you'd be right (on a couple songs). The fact remains that CoB are a combination of many different styles, including punk (by far the most underrated influence), and they don't sound like any one band.
To the IF dude: I specifically named one of their earlier songs, the Jester Script Transfigured. So if you like it, you must like "techno garbage", right? Or maybe you don't like it. But you almost definitely have a double-standard. In any event, ignorance prevails!