The only issue I have with Twilio is their charging. For voicemails, calls typically last less than 10 seconds, and often only a second (because they hang up and don't leave a message) - but as they charge per minute you are billed the full 60 seconds each call.

I built something similar as a side project but switched to Nexmo, purely because they charge per second. It was a fun thing to build and test.