I had a dilemma about this until very recently.
Having a 70" Sharp Aquos TV for a couple of years (good display I must say) and a Sony HW55ES Projector, with a Prismasonic anamorphic lens at the same distance, I wanted to move on to 4K.
I bought around 100 UHD's over the last 2 years, they come with the blu-ray version anyway in most cases.
A 100" electrical 2.35:1 tensioned Draper screen comes down in front of the 70" Sharp with only an inch of separation which results in an approx. equal viewing distance of 11ft. The screen is exactly 2:35m wide and 1m high. Downside, 16:9 projection is somewhat on the small side.
Most of the time my wife watches TV, series and an occasional movie on the 70" Aquos where I watch TV, series and practically all movies through projection, including 3D. Both give a very good experience although projection rules, especially with 2:35:1 movies but that's no secret
The setup is in the living room but light can be controlled adequately for projection although certainly not at bat cave level.
So, moving to 4K created a dilemma, which technology would get a 4K upgrade first? The TV or the projector? My requirements where kind of clear since day one, very good contrast, popping colours, future proof as much as possible with respect to the different HDR standards (HDR10, HDR+, DV, HLG), 3D and at least the same display size within a budget of around 6000 EUR (7000 USD). In case of a projector upgrade, lens control and lens memory where mandatory since the idea was to get rid of the Prismasonic and to add a dedicated bigger 16:9 electrical tensioned draper in front of the 2.35:1 screen. In case of a TV I preferably wanted OLED.
The extra screen was not foreseen in the budget for now. All criteria, of course, are the same for both technologies.
These 2 choices I caught sight of: Sony XBR-75X940E (75XE9405 in Europe), OLED prices are a killer at that size range and going smaller can never be forgiven. For the projector I wanted the SonyVPL-VW385ES (VPL-VW360ES in Europe) Which one first?
After a very long deliberation, endless comparisons, I ended up buying the TV first, no 3D though on 2017 TV's which I really cannot understand. After all I wanted the extremely good contrast and colour pop, the future proof HDR varieties and the TV screen size increase first. I don't even want to mention the 18Gb/s HDMI thingy here. Then the price difference was also kind of heavy, the Sony VW385ES was 1.5K EUR (1.8K USD) more than the TV and that's a lot of UHD movies on disc. Let me also say that I could sell that kind of upgrade to SWMBO better
In short, I still watch 2:35 movies, including 3D through projection but all the rest is through the 940E. With the black bars being really black, watching an occasional movie on the Sony 940E is also a treat. Also threw in an Apple TV 4K and replaced the Apple TV 4th Gen.
Projection is more impressive because of size but the contrast, peak luminosity and colours are just phenomenal on the Sony TV.
Already preparing the budget and the SWMBO sales pitch for the next upgrade in 2018