The 5800X3D +4000 would then be the 'cheaper' option although you very likely need a PSU too.I plan to do both. I currently game at 1440p on a 165hz monitor. Whilst my 5700xt has been serving me largely fine for that purpose, I would also like to game at 4K on a LG C2 (Dual monitor setup ; 1440p for work/competitive gaming and OLED for story games/immersion). As said, that obviously points to the next gen. The problem is, I'm a rather impatient person for one, and secondly, am concerned about using a new gen at launch that will require DDR5 and would possibly be susceptible to reliability issues of the new socket/gen. Another option I've been flirting with is staying on AM4 and going 5800X3D and then just upgrading the GPU to a 4000 series or 7000 AMD. That would save me having to get a new motherboard and RAM and should still fully push a next gen GPU seeing as we may be looking at 'only' a 10-15% increase on next gen CPU's (probably around 10% compared to 5800X3D).
I'm probably just being impatient and overly tight though. Going full next gen is very likely the best option. Although I doubt I would have the patience to wait for a 3D 7000 series chip as I highly doubt that will be available until some time after original launch of the new gen. Would probably just go with a 7900x or something.
The very best option is to wait for second gen on AM5 to get an even larger jump and DDR5 with much tighter timings. But there's no way in hell I'm waiting that long.