Been using both since they were each released, respectively. For some context, I am mostly a virtual instrument designer by trade. I also do a lot of sound libraries and ambient soundscape stuff. I'm designing instrument libraries for both Alchemy and Iris right now.
Alchemy has been where I spend about 90% of my day for general sound manipulation, it was kind of a dream come true for the kind of work I do. As I spend more and more time with Iris lately, I am seeing that they are filling two fairly distinct needs for me. I'm not seeing much overlap between them, at least not as far as how I'm using them.
I think it's fair to say that Alchemy is vastly more powerful, for lack of a better term. It just does a whole lot more stuff. Insane modulation capabilities, more synthesis/sampler types, more filters, more effects, more everything. On the other hand, Iris only does one thing, it just happens to do it really, really well.
The only major functional thing they have in common is that they both do spectral synthesis. And, in my opinion, doing spectral synthesis in Iris is just a better experience. It's more responsive, sounds superior, is faster, and just overall… better. The spectral features of Alchemy have always been a weak point for it, and I tend to avoid using them. It's a bit fiddly to deal with, very CPU hungry, and the sonic results aren't always so hot. That said, it's still capable of crazy good spectral stuff, due to the sheer overall power and feature set of Alchemy as a whole. But talking purely about spectral synthesis, I think Iris is better.
Spectral aside, nothing holds a candle to Alchemy in terms of granular synthesis and sound manipulation. It's a powerhouse and a workhorse for me. Bang for buck goes to Alchemy, hands-down. If you need to only do spectral synthesis, can't go wrong with Iris.
Hope that helps. A little time with the demos of each should give you a better idea.