There's two parts of concern when using AWS:
1. They comply with quite a number of information requests [0], even if they seem to oppose the weakening of legislation in place or overly-broad requests.
The NSLs under FISA are particularly concerning, because they can't even report the number they receive, only "within certain ranges set by the government". This is the same for all US companies, and Amazon are more upfront than most, but it's also a reason for avoiding a US company like Amazon.
2. Location. Where is your data? AWS' regions are quite broad in the legal sense, and sometimes crosses borders that your data would not be allowed to (X-data must remain in Y-region, cannot be copied or transferred). However, determining whether or not your data would cross such a border can be quite difficult.
[0] https://aws.amazon.com/compliance/amazon-information-request...