I use Stingray in a personal capacity as well as a Riverbed employee, so I'll share my comments from that perspective. I'm not very familiar with Barracuda, so I'll highlight what I like about Stingray:
#1: The scriptability. There's lots of load-balancing proxies that perform some sort of ADC functionality (compression, caching, bandwidth control etc) and Stingray matches all of those. Where it stands out is the ease of use of TrafficScript. It's fairly easy to understand what's going on (current activity and connections reports), and TrafficScript then makes it almost trivial to fix up problems with content or in test-and-dev sites where links or host headers are incorrect. The standard ADC features are so much more useful when you can drive them programmatically
#2: Software: I have dev versions of Stingray running on my laptop and on several dev machines in the lab. I could not do that with a paid-for or hardware appliance. I appreciate that Stingray runs on a familiar operating system (Linux) so I can use familiar debugging tools and familiar network/kernel configurations
#3: The UI: particularly the diagnosis page and status applet; I rarely find I have to dig round the UI to find the configuration problem or error that is causing problems.
In my experience, Stingray does just work. It's been solid and reliable and it's helped me fix application problems with ease that would have been really challenging if I had to go back to the application code and fix that myself.
Finally, I'm working on tidying up and reorganizing the Stingray content on splash.riverbed.com to make it easier to find the solutions that Zeus/Riverbed/customer have shared, so that you can get a better sense of what is possible