The upgrade CPU wise is pretty significant, if the prices are similar, I would definitely go for it. Just make sure you realize though that there are a lot of inconveniences when switching from one server to another.
Speaking strictly from CPU performance, I would guess yea, probably twice as good. Maybe even a little more than that. The X3220 is a pretty strong CPU. Make sure though if you're upgrading because of current performance issues, that you are also considering your current RAM usage and disk I/O speed.
The first thing you should ask yourself is, "Do I need to upgrade?" You'll always be able to find a better deal somewhere, if you look long enough, but whether or not you need to upgrade should really be the deciding factor. If your current server has met your requirements, continues to meet your requirements now, and as best as you can see will meet your requirements in the future, there's no point in having to move everything to a new box and possibly encounter new difficulties or cause more problems.
It definitely worths. Xeon is a server process. Athlon is made to power PC.
The X3220 is just a Q6600, nothing and 100% nothing is different from the Q6600.... just the box and the print on the IHS. So in simple words: It's a desktop CPU with the name of a server CPU.
Just like the Xeon 3040 = E6300, Xeon 3050 = E6400, Xeon 3060 = E6600 and there are many more examples.
To the TS:
That X3220 will just blast the X2 3800+ away. Basically the x2 3800+ runs on 2GHz, the X2 6000+ runs on 3.0GHz.... The x2 6000+ gets outrun by an E6600, the X3220 is 2 E6600s in 1 CPU. So you will have more speed & double the power of the speed.