So, your image size will be 16:9 aspect ratio and at 3m wide will be 1.69m tall. That's the math when you have a 16:9 projector.
If you don't have more than 3m of width to work with, or can't move the projector closer than 4.5m, then you could have an issue with the TK850 as it needs a bit less distance (lens to screen) to get a 3m wide image. It must be closer than 4.4m lens to screen, and should be 4.3 or closer for best results.
Either way, I would get the Epson. It will have better colors and better contrast than the DLP model. The TK850 is really designed as a 'bright room' projector.
For that matter, so is the Epson 3800. While the extra lumens are nice, it adds noise and heat in the room to deal with the extra brightness. The Epson 3200 may be a better choice for that room on that screen size.
I'm not sure what you are doing for lighting in the room, but I would take a close look at doing good directional lighting so you can have some lights on while enjoying the film.
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