The projector has nothing to do with whether or not it will be suited for a room with poor light control, sure a brighter projector can make the whites and colors pop more, but the blacks won't be there since there is no way to project anything darker than is what on the wall already, if that is a white screen, (typical) then your black levels will suffer tremendously.
I just got a 4000 lumen projector and tested it out in our living room, white walls, white ceiling, and a light rug on hardwood floor, the blacks were so bad that my wife went back to watching on her 27" iMac vs on 120" projector screen. I am no expert on TV's, but a family member just picked up a 75" samsung that he said was $2200 at Best Buy, he isn't the sort to shop things out at all, he just walks into a store, when his wife says "yes" they buy. My wife and I almost bought a 70" tv on Black Friday last year for $1200, maybe after the crazy deals ended, you still can't get one for $1500, it was an assumption, I could be off base.
Painting the walls darker will help greatly, but the biggest thing that helps is the floor and ceiling, this is because there is a lot more light from the image that gets closer to these than the walls. If you think about it, with a 100" image, you will have about 87" of image that is about 1-2ft away from the ceiling, on the walls, you have 49" of image that is typically several feet away from the nearest boarder. The washout that occurs nearest to the screen is most serious but the whole room affects things a lot.
Don't get me wrong, I really enjoy projectors, its great when people make the step into large screens, I just want you to be happy with the results and understand what the results will be if you take this route. There are also some great paints to look into that use grays that can greatly help black levels in rooms without perfect light control, use this with a nice bright image (which you will likely have at 100" diag) and you may get some very pleasing results.
A have a couple of very good friends from back in college who I helped to get a projector several years ago, they re-did their basement with dark walls but very light maple floors and white ceiling, the image the got was definitely washed out and did not demonstrate the projectors excellent black levels, however, they didn't care one bit, and I doubt most of their friends cared either, they LOVED having a nice big screen.
The other thing that plays in is light spillage from other rooms, even when they had all the lights off in the projector area, if one of them would open the bathroom door, or even have the lights on upstairs with the open staircase, the image got a lot worse. They had a very nice wet bar as well, when they turned on the can lights over this area, it made the image on the PJ downright unwatchable.