I faced this problem myself and decided to try Fisher's exact test. This has the advantage that the arithmetic boils down to something you can do with JavaScript. I put this on a web page - this should work either from there or if you download it to your computer (which you are welcome to do). I think you have a total of 382 successes and 7 failures in the old version, and 223 successes and 0 failures in the new one, and that you could get this at random with probability about 4% even if the new version was no better.
I suggest that you run it a bit more. You can play about with the web page to see how the probability changes if you survive longer - I would go for something over 1000 - in fact I'd try hard to turn it into something I could run automatically and then let it overnight to really blitz the problem.
