The AR100U was built I have read for ambient light rooms or very large screns. That isn't to say you can not make it work. If is too bright can add light filters to the lens to dim it down. I have no experience with either projector.
DLP doesn't have issue's with dust blobs in general as it is a sealed system. DLP also handles fast motion on screen the best as a single pixel will change at .08ms vs .2ms of the fastest LCD's. LCD's generally are brighter and come with lens shift allowing easier placement. A bright DLP in these price ranges are Pro8200 by ViewSonic, H6500 Acer. Recomend reading on the Mitsubishi HC4000 too. The HC4000 is the dimmest but will do a 106" screen in a light control room easily.
Some times you can find Optoma HD33 3D projectors in your price range too.