Yes, I believe you will need an adaptor to connect the P.W. to the flash. Shouldn't be too expensive, not compared to the price of the P.W.s anyway.
Yes, the ST-E2 will fire the flash wirelessly without any adaptors.
Here are the main differences, as I see it. The Canon wireless set up will let you keep the E-TTL metering, just like if the flash is on the camera. You can use up to 4 flash units and you can even set the power ratios from the master unit. The short coming of this system is that it's an IR signal. In some situations (outdoors) you may need line of site from sender to receiver for them to trigger. Indoors, the signal will bounce off the walls etc.
The Pocket Wizards are said to be very reliable. They are a radio wave signal so they should fire from just about anywhere. I think the range is also greater than the Canon IR system. The problem with this is that you loose the E-TTL metering and you have to set the flash power manually.
Either way, these two options are not cheap. Rather than buying the ST-E2, you could get another 580EX or another model (550EX, 420EX, 430EX) and use it as a slave...to your 580EX. Your flash can do everything that the ST-E2 can do.