Well, the answer is the classic “it depends”.
Let me breakdown a bit your question.
My technique has, as most raytracers, two stages. One to build the acceleration structures (voxelization in my case) and another to do the tracing.
Only the first stage is dependent on the geometry, and is linear in the number of primitives and triangles per primitives. Then the raytracing stage is constant on the scene geometry.
Complexity scales linearly to the number of pixels to be traced, so in 4K you get 4 times less performance. Keep in mind that the tracing is done on a half resolution buffer.
I get about 12 FPS down from 52, almost exactly 4 times slower, on a high quality preset with my GTX 750 Ti at 4K. But you won’t game at 4K with a 750 Ti…
Later I plan to divide the voxelization in a bunch of diferent stages, so that only the things that really need to be voxelized get voxelized. For now it sends everything every frame.
EDIT: Considering that at 4K the GI buffer ends up at 1080p, wich is quite overkill, you could trace at quarter resolution when rendering at 4K, and you should get the same performance that running at 1080p