I've owned both. It really comes down to musical preferences, system synergy, and room, not necessarily in that order.
I found the AM Stealth to be more dynamic, transparent, quick and agile. While the Shunyata Hydra's strengths are rich, vibrant tonal qualities, fuller bass (not more extended, more abundant), soundstaging. Note, I am comparing the Stealth with the original Hydra, not Hydra-8 or AM Matrix. The Stealth does have surge protection, the original Hydra doesn't, if that matters to you.
Weakness'? The Stealth can sound thin and analytical. The Hydra can sound thick and slow.
So it depends on what you're looking for. It's similar to SS (AM) vs. Tubes (Shunyata) debate, IMHO.
I hope this was somewhat helpful, currently, I am enjoying the Hydra.
Happy Holidays,
John