Is this an either/or situation, where you want to ditch or replace your projector with a TV? If not, I’d suggest sticking with a projector for those times when you would like to watch with the lights off just for the immersion, and have a TV for all those other times.
HomeTheater
I'm about to set up an outdoor entertainment area. Do you think a TV or a projector would be better? I'm weighing up the extra size from a projector versus the clarity of a TV.
How much space do you have? Do you intend to use it mainly after sunset (which could be 9pm+ in the summer depending on where you are)? By outdoors, do you mean a sheltered area (do you need the equipment to be portable)?
The space is only large enough for one of those stereotypical school projector screens, but that's still much larger than a tv. The intention is to use it after sunset in an area lit by fairy lights. Do you think that would adversely affect the viewing? The area would be exposed to the elements, so I'd have to move and store the tv/ projector when not in use.
If there are fairy lights, it might affect the color a little bit, depending on the brightness of the projector. This depends on your budget - anything decent should be fine, you just can't get the cheap $250 Chinese ones. It's also a solveable problem, since you can adjust the brightness/direction of the fairy lights.
Having to move and store it would be the biggest concern for me. A projector is easier to pack and unpack, but has the issue of a separate projector screen.
If you're able to, say, use one flat wall as a makeshift screen, I'd personally choose the projector.