Hey Adam -
Unfortunately, once charcoal has been fully lit (covered in gray ash), it lends no inherent flavor to food, and neither does gas. That is where wood chips, chunks, etc. come in. The "smoke ring" that Doug is talking about can occur in a charcoal or gas environment, as burning these organic fuels generates Nitrogen Dioxide gas, which in turn dissolves on the meat's surface into Nitrous Acid, which then works it's way into the meat tissue and finally is converted into Nitric Oxide, which affects meats in the same way as Sodium Nitrite (found in hot dogs, most sausages, etc.) - it turns it pink! (On Food and Cooking, McGee, 1984)
What people commonly associate as the "grill flavor" (as opposed to wood-smoked Barbecue flavor) is what happens as a result of the food juices and fats dripping onto the charcoal or gas grill bars and vaporizing, sending up "smoke" and steam. Some of this "smoke" ends up sticking to the food, and thats where you get that charred/bitter flavor. If flames are licking the food (bad), that's where you get that super-intense bitter char flavor (ex. Burger Kin&).
That being said, if you are just grilling the Brats, since the Brats only have to be on the grill for a short time, I would use the gasser. If you decided to sex it up a bit and you wanted to have a pan of beer and onions simmering to hold the Brats in until dinner's ready, then you could go gas or charcoal since you'll probably be on there long enough to make lighting up a load of charcoal worthwhile.
Now if you really wanted to go all out and get some real smoke flavor on there, you will have to cook the Brats for at least an hour in a lid-on, woodsmoke-filled environment. I say at least an hour because once you have committed to using wood chips or chunks, food has to be covered and exposed to smoke for at least an hour or more for it to pick up any smoke flavor.
But hey, if you can achieve low enough temps on your sexy new Performer long enough for the Brats to be in there for an hour or more, I say go for it! That's half the fun of being on the Weber - being outside playing with fire as long as possible.
Fire up the Performer with probably a third to a half-load of charcoal (depending on your climate) banked to one side, all vents fully open. On the opposite side have a pan with water. Once the charcoal has ashed over, throw some soaked chips or a dry chunk on top, and cover until it starts smoking. Clean your grill grate, then place the Brats on the side opposite the coals over the water pan. Completely close the bottom vent, but leave the top vent fully open, and position it above the brats. At the half hour mark, check the brats quickly to see how they are doing, make sure that your wood is still producing smoke, and that you have enough charcoal going to last at least an hour to an hour and a half, then re-cover. Once they reach 155 and no more than 160 on a instant read or meat thermometer, pull them off the grill and allow to rest for five minutes before you tear into them. The goal is to allow them to be on there for as long as possible, but you don't want to dry them out. The water pan helps with that.
Final thoughts; casings can definitely be a flavor bummer, especially if your respective other likes to cut them off. Casings definitely act as a flavor and smoke barrier, just as the skin underneath a beautiful rack of ribs will. If you have the time (and raw Brats - this does not apply to "fully cooked" crappy Brats), allow the Brats to hang or lay on a rack competely uncovered in your refrigerator overnight to allow the casings to dry a bit and become tacky, aka "to develop a Pellicle". This in turn will make it easier for smoke to attach to the Brats and will also "thin" the skins enough for them to be more palatable so you can actually eat that smoke flavor and not throw it away. Enjoy!
I look forward to seeing some pictures!