Only build what the camera sees.
- Once said Nathan Wells, in his perfectly done "Bricks in Motion" tutorial series. (Which I'd really recommend any brickfilmer to watch, BTW) Though he used a webcam in that video, the rule applies to any camera that you could use for a film - You don't need to build some big, awesome set, just to have 1/12 of it appear in the final film. Instead, write things out, make some concept art, draw an over-head view of the sets, and make it in LDD - that way, you not only end up with better, more original set designs, but you also use less LEGO bricks, and just build what's right for the shot itself - a luxury that only animation and stop-motion really have.
Thus, if you're going by Nathan's rule, you could really use any camera for brickfilming. The only problems come down to filming on already made sets. (which, really, should be carefully dismantled for each individual shout, even though most of us brickfilmers are too lazy to do that, and just try to film the best we can on what we already have) However, with a dslr, you can usually have much more control over things such as aspect ratio, size and image quality, zoom features, and even can mess with setting the picture-capture on a timer! Most, if not all of these things could be done with a decent webcam, and some heavy editing in post, however, the dslr would cut down the time you spend editing tremendously!
Thus, that's really a hard question, togfox. Both cameras have advantages as well as disadvantages. Only when looking into minor details and set-ups does the dslr usually come out ahead. It really all boils down to how much money you've got in your pocket, and if you're willing to change to be a better brickfilmer? (Not to say that great brickfilms haven't been done on webcams, as, they will no doubt continue to be made on them...) If you can invest in a dslr, it's probably for the best if you're going to use your LEGO collection to it's fullest, and dismantle sets just to get the perfect shots in your film. I you're going to be filming in tiny sections, with the camera close to the actual set at all times, then a webcam is probably best. However, if you'd prefer to build simple wall-and-minifig sets, then, either would do you well.