A GTX 1660 Super is a very fine 1080p card. $230 or $240 for a twin fan model. Actually the twin fan one I linked apparently gets a $10 rebate, so is only $230.
There are cheaper options, or you could even go for an RTX 2060 (non-Super) now the prices have come down a bit, but a 1660 Super is probably as high as I'd really recommend for 1080p 60hz. The 5600 XT is in the same kind of ballpark as a 2060.
It's often not worth buying the more expensive models of GPUs than the cheaper ones, as the prices increase very quickly and there is little room between X GPU and the next model up (i.e. why spend $270 on a 1660 Super when you can get a 1660 Super for $230 or a 2060 for $300 for instance). Also there's relatively little performance difference between Model A and Model B of a given GPU.
In terms of the kind of performance to expect and relative to other cards:
The Radeon RX 5600 XT is a respectable product that has pushed for lower prices and better performance at $300. For that alone, we commend it. The...
Your 780 ti would be somewhere below a RX 570 in modern gaming I expect. (that was a guess but seems borne out by a Gamers Nexus benchmark - this article doesn't actually show a 1660 Super but 1660 Super is almost exactly the same as 1660 ti to give you an idea).
I agree with @Oussebon that a GTX 1660 Super is probably the best 1080p performance value at sub-$250 price points. How meaningful would it be to save $150 off of your budget? If you'd be happy to save that money, then think about a 1660 Super, or making the step up $40 or so to the RX 5600 XT. Those cards will average 60fps or above at ultra settings in most games.
You can go more expensive and more powerful and get an RX 5700 XT in the $350 price range, but you won't notice the extra performance 90% of the time at 1080p 60Hz, so you could argue that it's wasted money. If money really isn't an object within that $400 budget then maybe you'd want to get an RX 5700 XT as overkill insurance to make sure you never dip below 60fps, and for the added longevity before upgrading. I can't recommend this as a good value for 1080p, but it's an option for you within your budget.
These recommendations assume you are not wanting to go for Ray Tracing. I personally don't think the tech is mature enough yet for it to be worth it, but you might feel differently, in which case you'll need an RTX card, at least the RTX 2060, if not more since Ray Tracing is very taxing even at 1080p.
I don't think anyone in their right mind could argue that something like a 5700 XT would be good value for 1080p
Instead of buying ian overkill GPU as some kind of framerate insurance frankly the smarter play if spending the full $400 on 1080p gaming would be to buy a 1660 Super for $230, AND a 1080p 144hz monitor with adaptive sync for $170-180. Because then you'd need not worry about dipping below 60fps - because adaptive sync.
While also being able to profit from framerates higher than 60 thanks to not being limited to 60hz any more.
I have the same CPU as @Kevlee but an i5-4670K. I want to upgrade my graphic card. Right now I have a GTX 760. I only got $200 to spend on a graphic card. What would y'all recommend for that price? @Oussebon@Zoid