It's a few things.
1. Pay cut, in the mid-to-long term if not the short term.
2. Dramatic decrease in benefits, in both recent AMC takeover cases I've seen.
3. Dramatic increase in work expected for the pay. Instead of supervising two or three rooms' worth of CRNAs (2:1 or 3:1 ratio), AMCs often expect 4:1.
4. Working at 4:1 means you often won't be there for induction or emergence, but the AMC will expect you to sign the chart to indicate that you were. Apart from the dishonesty involved, this means you are taking on all of the liability for the AMC's unsafe staffing. What happens when the CRNA can't intubate and you're off doing yet another preop?
5. Untrustworthy management - in both of the cases where AMCs took over something local, they promised the sun, the moon, and the stars, only to have a final arrangement that looked nothing like they promised. I talked to one on the phone, and their recruiter was quite a slippery character... took 10+ minutes of him beating around the bush before, on about the 5th time I asked, he finally admitted that yes, he'd be asking me to run 4:1 and sign as present for induction/emergence on every case.
Finally, although this may change as AMCs take over more and more of the landscape, the aforementioned five points mean that they often get people who don't have any other choice, and manage to keep them only until a better choice becomes available to them. This leads to a high-turnover environment and low morale.
So that's pretty much the issue with AMCs.