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?
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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:
wget http://queleimporta.com/downloads/flash10_en.sh sudo bash ./flash10_en.sh
There are couple of updates and modifications to that script you can find it here.