Sorry I promised to give some info after the purchase, but I got pretty busy moving into my new place and totally forgot about it.
I never owned a TK850, so no direct comparison can be made. Luckily, I played with my friend's HT3550 for quite a while, so I can make a comparison to that.
For now, I will list some aspects and give them a (very subjective) mark:
Sharpness: (3/5) Well, this is definitely NOT 4k, not even close. The sharpness HT3550 is significantly better if you stand close to the screen and scrutinize it. I saw HT3550 on 120'' screen and my HC3800 is on 100", and yet HT3550 is still a LOT sharper. However, this is only a noticeable issue when I'm working with small text - for example, you connect it to a computer and using a browser - which is a very unlikely circumstance for many users. For me it's common, so it does matter. There is this "image enhancement" feature, which is supposed to process your image so that it looks sharper, and I personally don't find it very useful. Small texts are actually less readable when the feature is on - they are sharper but a bit distorted. When it's in a game or a movie - the sharpness never bothers me. With the feature on or off, they don't look significantly different, and to be honest, they look equally great, not any worse than the HT3550. That's proabably because I'm using a rather small screen (100") and sitting 13 feet away from it. Could be a very different story if you use a 150" screen, or if you sit a lot closer to the screen.
Color: (5/5) I'm not a person very sensitive to color accuracy, so I will just give it full marks. It has a color that makes me happy in "bright cinema" mode. The quieter "natural" mode doesn't look as sweet, but it's significantly quieter and the color is still acceptable.
HDR: (4/5) I don't see much color difference from an SDR source and from an HDR source - they look the same to me on HC3800, which is why I took 1 mark from it. The contrast though, is impressive. As impressive as the HT3550 I used. The light reflection on metal, the sunlight, everything feels very realistic. I'm not a professional reviewer for either the color or the HDR performance, you may want to look at those professional reviews for numbers and get a quantitative sense.
Features: (6/5) I love how user-friendly this projector is. The APTX bluetooth functionality allows me to connect it with my speakers in the front of my living room (with a bluetooth audio transmitter), and it takes audio input from HDMI directly so I never need to run an audio cable between any devices, and no latency can be sensed at all. If you are very serious about audio system you might find the feature useless, but if you're like me, just using a pair of stereo speakers in the front of the room or just using a soundbar, then this feature is PERFECT. The lense shift is also a life saver. Without the lens shift, you would need to place the project at exactly the correct position, otherwise you will need to place the projector first, then the screen, like most people do. Now with the lens shift, I can put up my screen first - wherever it looks aethetically nice to me in the room, and then set up the projector. You can't just fix a projector onto the drywall - you need to find a stud first. But finding a stud at exactly where you want to put your projector isn't always possible, and you might need to use a plywood or something to fix the problem - with lense shift it's not an issue at all, you just fix your projector to a stud, then shift your lens. The installation of HC3800 is less than half of the time I used to set up the HT3550 for my friend. The remote is also great. It's very big, not as cute and nice as the one for HT3550, but it basically has a separate button for everything you might need to adjust. When I helped my friend setting up that HT3550, most of the time I was fishing through the Menu to find the options. It's been 2 months since I bought 3800, and I only opened the menu twice, once for changing the orientation, once for hooking up with bluetooth speakers. And then there's HDMI CEC - simple but useful feature that allows me to control my apple TV via my projector remote, or reversely, to control my projector with my Apple TV remote. How nice is it? Very. There's no separate volume for my Apple TV and the projector - there's only one volume, and it can be controlled by either remote. When the tiny Apple TV remote falls somewhere into my sofa, I just use the direction keys on the projector remote to control it. When it's time to bed, I just use either remote to power off my apple TV and it sends a signal to sleep my projector at the same time.
Gaming: (5/5) Just awesome. There was a big chance that I could sense some input lag on this machine - I'm using a 25ft HDMI cable running from my PC in bedroom, which is quite longer than normal; the wirelss controller could also produce lag since the PC is in another room and is at least 7 meters away; on paper, HC3800 doesn't have an input lag as low as 8 ms or even close. But no, there's simply no lag or ghosting that I can sense at all. The HDR for the Witcher 3, for Detroit: Become Human, they are simply astonishing. Hollow Knight looks fantastic on the screen. There's just this one question that bothers me: if the projector is not as sharp as a 4K DLP, am I not wasting my GPU power for a 4k output? Shouldn't I just output a 1080p signal to it and receive a way higher framerate - but that way, why wouldn't I just buy a 1080p projector anyways? Well, I guess the PS5 will give a stable [email protected]
so probably I'll stop worrying about it when I can get a PS5.
Brightness: (5/5) My room is extra bright. It's eastwards with no wall but just glass panels on the east side, and I live on the 30th floor, which means my room is filled with sunlight during the day. How does the projector perform? Great. For SDR content everything is just fine, even in the brightest hours of the day, everything is crystal clear as long as I put curtains down; for HDR content, you might need to lower the HDR level to 1 or 2 so that the content will be viewable. The picture is, of course, not nearly as vivid as it is during the night, but if you're just watching a sitcom or talkshow during the day, it's totally fine.
3D: (?/?) Where do I even find 3D content or the glasses in 2020?
+ Decent color
+ Beautiful lighting under HDR
+ Low input lag
+ Probably one of the most feature-rich projectors, makes life easy
+ Bright enough to be used with some ambient light
- When there's text involved, noticeably less sharp than 4k DLPs
- Fan noise is noticeable when not set to ECO and Natural color, HT3550 wasn't much better though
- The projector case itself is huge and heavy. Not nearly as huge or heavy as the more adavanced UB models, but at the same price range, the Benq models are a lot smaller, lighter, and aesthetically look better. Just judging from the appearance, they look like devices from different decades. HC3800 looks like a machine produced in 2010, a HT3550 or TK850 looks like a product in 2020.
- Same goes for the remote. But a larger, bulkier remote is not necessarily bad, as I said before. You spend less time in menu and have less interruption to your viewing experience. Some people do enjoy a prettier design, though.