In terms of mechanics, the main thing Armageddon's Blade added was a new faction (the Conflux), along with a small assortment of new artifacts and creatures. The main thing Shadow of Death added was combination artifacts, again with a small assortment of new artifacts, creatures, and terrain types. Each expansion also came with a new campaign about equal in length to the original campaign. I'd personally consider the largest benefit being able to play some of the player-made maps requiring the expansions (and there are quite a few very good ones). It's also a good way to breath some new life into the game if you enjoyed it but feel that you've just about played it to death. If I had to give a shorter answer: yes, it's worth the $10.
As for HOMM2 compared to HOMM3, the mechanics are quite a bit simpler, but the game has a definite charm to it that's tough to put into words. Overall I like HOMM3 more, but still would highly recommend HOMM2.