1st a grand isn't budget, budget is 300 to 700 territory. A grand is entry level enthusiast
I did make the distinction of "home
cinema projector" rather than just "projector" or "home
entertainment projector"
This could be debated until the cows come home, and particularly so since the lines are becoming somewhat blurred; but in a quarter century of dealing with the projector market, manufacturers have always segmented their product offerings in to application classes. How a purchaser decides to use (or misuse) a projector is incidental and irrelevant really. The same goes for how retailers attempt to 'sell up' inappropriately. For example, just because a low-rent office projector has a video input, it doesn't make it a home cinema projector no matter how many superlatives are thrown in to the advert copy.
As I see it, the bulk of product between £300 and £900 falls in to one of two main categories. It's either an office projector or an entertainment projector.
Office projectors are those machines starting at the £300 end of the market where its either obvious they're no use to the home cinema enthusiast (e.g. 4:3 ratio, lack HDMI inputs etc) or they're just too cheap to incorporate decent video scaling and reasonable video contrast.
Home Entertainment projectors will have HDMI and a 16:9 panel, but they're geared for maximum brightness rather than video contrast. These are the Benqs, the entry-level Infocus, and a good proportion of the Optoma range.
Home Cinema projectors have something that sets them apart from the Entertainment brigade. It could be they use better light engines, superior lenses, better scaling, calibration features, or have higher intra-scene video contrast or better black performance. Whatever it is, it just takes the performance above the level of the next lowest stablemate. We'd probably have to agree to differ, but I don't see those qualities in projectors where the whole shooting match of pj, screen, bracket, cables etc can be bought for under £1000 any more than I'd put a Big Mac meal on a par with a sirloin steak restaurant dinner. Each has their place, and there's some overlap in what they achieve, but that doesn't make them the same in my book.