If you read the forums people are making amazing and hard to blielve claims about their grills. (cook a pork butt for 16 hours at 250F and the temperature never wavers and there is still 2/3 of your charcoal left unburned...)
I was in the same boat as you. I own a Bradley as well as a Weber kettle. I received a large BGE as an early wedding present and since then I haven't fired up either the Bradley or the Weber. The BGE is pretty amazing in terms of it's versatility.
I quoted the 250F for 16 hour comment because it can be done but I would argue not without the help of a DigiQ or some other controller. The BGE does hold it's heat very well and is pretty easy to keep fairly stable but with the DigiQ you can literally get it to temperature and not worry about it. It really does amaze me every time I use it. I had a PID for my Bradley but it had the problem of heat retention after the door was opened. The temperature recovery time for the Bradley is poor unless you do modifications to the chamber. No worries about that with the Egg. In fact, if you go way over in temperature with the Egg you will have trouble getting the temp back down because the ceramic holds the heat so well.
The grill size is limited versus other smokers as bigbump mentioned. You only have the one level to play with unless you get some aftermarket pieces. It's plenty big enough to do 4+ racks of ribs on a vertical rack or a pork butt and has plenty of space for normal direct grilling. You have a Bradley so this isn't a huge concern. If you are cooking multiple pork butts or briskets for a party you have ample space in there.
It holds moisture very, very well and seals nicely when closed. Again, someone mentioned the burping. This is necessary because it's sealed so well that when the cover is down there is no flames being produced. When the cover is opened, a large rush of air runs in and the flames come up VERY fast. It's cool and a bit scary at the same time.
For indirect cooking and smoking you should invest in the plate setter. It raises the rack and blocks all direct heat. It works very nicely.
I'm still working on getting a great pizza out of it but I know it's possible. It's pretty easy to push the temp up to 600F-700F. High enough to break a cheap pizza stone after only one use.
I don't think you will regret your purchase for a second!