The Ryzen 7 9800X3D is the better gaming chip, full stop. The real question isn't which one wins, it's whether winning is worth $96 more at today's new prices.
What the extra money buys
New, the 9800X3D runs $96 over the 7800X3D on ChipFlip's own tracked listings, a 28% premium. TechSpot's testing puts the 9800X3D about 17% faster on average across a broad game suite, with the gap swinging a lot by title: Counter-Strike 2 and Fortnite both showed solid double-digit gains, while some Assassin's Creed games barely moved. That's not a small detail. A flat "17% faster" number hides how unevenly that gain actually lands depending on what's in your library.
Where the 9800X3D actually earns it
240Hz esports titles, sim racing, and late-game strategy titles where CPU load spikes hard are where the extra cache shows up as real, felt frames. If that's your genre, the newer chip is worth chasing.
Where it doesn't matter
At 4K, the GPU is doing the heavy lifting regardless of which of these two chips is behind it. The performance gap mostly disappears into rounding error once the graphics card becomes the bottleneck, which it usually is at that resolution. Buying the pricier chip for a 4K build is paying for a difference you won't see.
The takeaway
If you're building fresh and chasing every frame at 1080p or 1440p high refresh, pay the $96. If you already run a 7800X3D, there's no real case for switching. And if 4K is the target resolution, save the money entirely and put it toward the GPU instead, that's where the frames actually come from at that resolution.