Something is seriously wrong with this picture - go to Twilio.com and go to Tropo.com... anyone else is seeing doubles?! Voxeo seems to be in the copycat mode here...
Back to the subject of the question - from what I know Twilio uses Asterisk as the core of it's services, but they have written a lot of new stuff. That's why @sipwiz doesn't think they are based on Asterisk. The TTS engine sounds like FreeTTS I've used in the past on my own asterisk implementations. It's not the best out there, but does the job and like the name suggests - free. Not sure what they use for speech recognition though.
I have to admit that I'm a fan of Twilio - we currently route significant amount of traffic (in tens of thousands minutes per month) through them and so far nothing but good. The team is super responsive and a pleasure to work with.