tweepy has a larger userbase and is more actively supported. Also, there are certain foibles with twython's streaming class that may not be issues with tweepy. Namely:
The streaming class shouldn't need to be associated with a twitter account. That doesn't make sense. I think this is related to why I keep getting 420 errors.
I don't see any way to access the response header, which means I can't access any rate limiting details (again, probably would help with the 420 errors).
tweepy has a larger userbase and is more actively supported. Also, there are certain foibles with twython's streaming class that may not be issues with tweepy. Namely: