Performance-wise they seemed mostly similar - both can pick up text fairly accurately in somewhat noisy environments. We did notice that Google's offering seemed to be slightly more accurate. But the difference was marginal and only noticeable when we compared side-by-side on intentionally poorly pronounced words. There were two big differences that made it impossible for us to use Google's product:
1. Google has a 1 minute limit on streaming speech-to-text. It just closes the connection at 1 minute. It doesn't even send you a "final result", so if speech was being recorded at the time the connection dropped, that transcription is lost. Speaking of which...
2. Google doesn't provide incremental updates. So if someone speaks for a while, you only get an update at the end of it.
Note that this is their API - my impression is the product they use in their apps is superior in functionality to the product available on Google Cloud.
Amazon Transcribe, on the other hand, has a 4 hour limit and sends incremental updates, so in a longer sentence, like this one I'm currently writing, you would get a message every couple words, which is essential when the goal is to show a live transcription.