There really isn't a clear winner since both have a few games where they just crush the other. The average is close enough that it may as well be margin of error.
However, at this point in time the AMD CPU and DDR4 memory are considerably cheaper. Even if you do play one of the titles where Intel does win by double digits, is it worth the $400+ it will cost for that?
If you already have an AM4 board there's good odds the 5800X3D is supported. HUB did some testing for Zen 3 on old X370 boards and found that there's maybe a 1% performance loss on average over the newest boards.
Unless you're a competitive CS player, it's hard to justify the extra cost for Intel. You'd be better off just getting something like a 12400 which will get you most of the performance at a much lower price and event upgrading to a 13000-series CPU.
AMD already bumped prices with Zen 3, to some degree because they could, but their costs aren't going down with Zen 4. The chiplets aren't any really smaller even with the move to 5nm and the IO die is using a much more expensive process now as well. Maybe AMD uses the Zen 3 cost jump to eat those extra costs, but there's no guarantees there. However, I don't think Intel can keep charging several hundred dollars more than AMD if they hope to be any kind of winner beyond on paper.