Interesting. I've always had much better quality using Twilio to bridge to PSTN than through Twilio Client.
I keep coming back to Twilio Client because the idea of a softphone (and a web based one at that) is so alluring compared to having to deploy more hardware.
If I recall there was also a cost advantage to using Twilio Client (you only have to pay for one leg of the call instead of both legs).
But every time we've tried to deploy it there have been quality and usability issues which have forced us to fallback to PSTN. Never the less, I'll keep trying it every couple of months... :)