DLP vs. LCD is a long debate. In a nutshell, DLP has simply been pounded by LCD at the mid-range level. There are few DLP projectors with decent lenses that allow for long zoom range and reasonable lens shift. The other issue, especially with the newest DLP models, is that their contrast is weak. The newest DLP chips have lower contrast than the 1080p chips they had before. So, higher resolution, but lower contrast. That's a big tradeoff for anyone in a good room.
But, at the lower end, DLP tends to outperform LCD, and you can't touch the price for 4K resolution models. DLP is a good deal less money.
LCD has no chance of rainbow effect (RBE) which is good. Their colors are typically excellent and considered to have better saturation, but this is very close these days.
LCD is brighter. Almost ALWAYS LCD is brighter than DLP.
This has to do with color brightness and there is a lot written up about color brightness vs. rated brightness. For example, that 3,200 lumen Optoma, once calibrated for decent color is likely to only deliver about 1,000 lumens of calibration brightness. In comparison, the Epson may deliver 1,400+ lumens, and can reach beyond 2,000 lumens while still maintaining excellent color. The Optoma simply can't. This is all about color wheels and color wheel speeds and marketing.
Have NO doubt that when a DLP projector talks about 3,000+ lumens, they are using MARKETING, not actual performance on that number. A good home theater DLP will be about 1,200-1,500 lumens. That's plenty. LCD can get 25%+ brighter, but that's still plenty.
Stop talking about 'living room' lighting. These are projectors. No theater you walk into will have big windows streaming in sunlight. They have NO windows. They turn the lights off. They use dark furniture. It's a completely different discussion when you compare a living room setup vs. a home theater setup. Lights kill what front projection does and the contrast ratio of 1,000:1+ will drop to 50:1 or less very quickly.
But, your comment about worrying about watching sports with some lights on is a good question. It, of course, has nothing to do with your projector and EVERYTHING to do with how you light the room. I have an example of how to properly light your room:
http://www.avintegrated.com/lighting.html
Don't screw up your lighting and you can use a relatively dim projector and still have excellent results. Directional lighting that is away from the screen will keep the on-screen image looking excellent. But, any lighting that falls on the screen from wall sconces or ceiling flood lights is not the right way to do things while the projector is on, and it is something that is in your control.
As to size: If you are ceiling mounting, it just doesn't matter. All the top-shelf projectors are large... why is that? It is because larger projectors offer better cooling systems with less noise and it allows for a better optical system with more lens shift and better lenses to be in place. So, almost all large projectors will be quieter than their smaller counterparts. This allows them to run cooler overall as well which can help the electronics to last longer. The lens system is pretty straightforward as you will find that Sony, JVC, and Epson in their larger models all have MUCH more lens shift and zoom range than the cheaper and smaller DLP models. Larger size is good. Sure, it may not work for someone who wants a quick and dirty on the table setup, but for those installing from a ceiling, or a planned setup, it's just a non-issue.
All of this kind of dismisses the JVC and Sony projectors which use LCoS technology. LCoS tends to be dimmer than LCD. Similar to most DLP models around 1,400 lumens or so. But, the contrast is much higher than what LCD or DLP can deliver with the same high color saturation of LCD. It's just more expensive to get into LCoS.
A dedicated home theater deserves a very high quality projector. The Epson 4010 is a decent one. For the money it is solid. But, it's entry level 4K. Lower mid-level at best. If I was buying and that's all the money I had, then I would get the Epson for a dedicated theater due to the lens shift, brightness, and solid contrast. But, I would more likely get a used JVC RS420 or RS440. It would give me better contrast and higher quality for the money. Preferably I would save up for a newer true 4K projector from Sony or JVC.
I don't buy for aesthetics really. I buy to get the greatest performance that I can for the space I have. Sometimes this forces my hand, but when I can make the situation my own, I shoot to get what will give me the most I can hope for.
Dark paint, dark carpet, dark walls and ceiling, dark furniture, and a good LCD or LCoS over DLP is the only way to go at this time for best performance. DLP is great for all those just getting into the technology who want something for their living room or have a very tight budget.
