I only just now downloaded the Hydra software so I never actually used it.
with that said,
Hydra = $1750
AEM = $1700(ebay)-$2000
Dollar for Dollar the AEM
looks much more refined and user friendly. It looks like the Hydra has most of the capability of the AEM but the control interfaces aren't just defined. The Hydra looks like it can do Staged injection, traction control, NOS, water injection, 2 step rev limiter, ect, you just have to do all the work to define the multiple I/Os and required mapping. Versatile for sure, but the Hydra just takes more thinking or more $$$ to have someone do it.
If you had an odd ball turbo V6 or V8 it looks like it fill the bill pretty nice. I especially like the built in Dual wideband control/trim. I definately wouldn't recomend it for a first time user though.
The AEM is pretty much ready go, and for nearly the same price, I don't see any advantage to the Hydra.
Here's a good review of the Hydra with good comments by several guys with more experiece than anyone here put together.
Hydra Review