When I encounter a flash video in ubuntu I get an option to install 3 different swf players:
Which is the most stable and preferred player?
It might be slow but it's still the best of the lot still for feature compliance and stability.
You forget Lightspark. But none of these alternative is really stable and they will usually work on few videos and crash on the others. If you watch lot of video I suggest you stick to Adobe Flash, if you don't watch a lot of videos and don't play online flash videos games Lightspark and Swfdec are good.
It really depends on many factors. I have the best user experience with the Adobe version.
However if you are using a 64bit version of Ubuntu, it might be tricky to set up Adobe flash. There's a shell script that helps you in that process. Download it and use these commands in terminal:
There are couple of updates and modifications to that script you can find it here.