The modern projectors you're looking at have nearly double the brightness of your old projector (in practice, that's almost as bright as you can go in this price bracket): but I suspect it's still not going to be sufficient if your results with your previous projector were that poor...
Unless you have a means to drop the amount of light landing on the screen area to the point where you'd have trouble with, say, reading against the wall - then the image is going to wash out pretty badly during the day.
I'd stick to your flatscreen for daytime viewing.
A dual-setup, however, might be an option (TV for the day; projector at night) if you can make a plan to do so in your room.
BenQ HT2050 Projector; Kodi (on Ubuntu, OpenELEC & S802) via Sony STR-DH540 AVR with Boston Acoustics SoundWare XS SE 5.1 Audio + Jamo 210 Sub. Emby for Mobile Streaming.
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