There are a lot of problems with RTX performance right now, honestly I'd be cautious of that dumpster fire until Nvidia figures out what's going on and fixes it. A lot of people are getting 1070 ti or 1080 performance out of 2080s for no discernable reason, the 2080 ti founders cards might have a very severe issue with memory/VRM cooling and it's unknown what other cards (if any) that affects, there aren't any RTX games out right now and it's unclear whether the performance hit is small enough for it to be worth anyone's time. IDK, it's not a basket I'd put my eggs in yet. Maybe in a month or two they'll have all this stuff sorted, but for now it's a very expensive, very immature platform and it's kind of hard to tell if the cost will be worth it in a year's time.
A 2080 or 1080 ti will be fine at 4k, I don't know why people fret so much about "turning down the settings" by running 2x anistropic filtering instead of 16x at 4k (which makes almost no difference at all) or running some parameters at high instead of ultra, it's still a great experience.
I guess if they're the same price, I might steer towards the 2080, but be prepared to ship it back asap if there's something that you don't like about it or you have a problem. You shouldn't put up with being a guinea pig after spending $800+ on a graphics card.
Also, be aware that neither of these options is going to provide you with top tier performance for 5 years. That's a long time in graphics card years. The 2080 might have an aging advantage considering Nvidia's track record of not providing driver optimizations for older architectures (just look at the 780 ti), but it's really hard to tell.