I've never tried using the video download extensions, instead I look in my Firefox cache folder to retrieve the videos. Back to the topic, I'm currently using Firefox. Chrome is too bland for my liking, not to mention I don't support a company that has a mission to dominate every market.
The new FireFox 4 is, well I wouldn't say as fast as chrome but it is definitely on it's way. I'm now using FireFox 4 Beta 8, shits hell faster than FireFox 3! Oh, and since firefox is not as fast as chrome, I'm sure the custom themes and better features make up for it.
It is not my specialty to know about web browsers, but what I know is that everything depends on the speed of your connection and your computer settings
For me, Firefox works better