I just dug up one of my sources for you, you'll enjoy this.[0] It may no longer be accurate but it's at least suggestive. They all have similar latency, but you'll see the in the longest delay results (my eyeballs always focus on worst-case), has the software encoder on top. I'm currently considering a 5800X (higher sustained boost clocks due to heat/VRMs) or 5900X (lower sustained boost but more cores for potentially better streaming) to upgrade my system.
Given an 8+ core system can encode so well, I'm fine with either a 6800XT or 6080. I really don't have enough information yet. For years I used to buy based on NV's OpenGL support (and after NV's Vista driver blunders, AMD), but since the Oculus Quest was released, my primary deciding factor is VR performance. NV has held the edge there historically, but 16GB VRAM for the same price is not to be dismissed outright. If NV will match AMD's 16GB at a similar MSRP I'd go that route, the GDDR6X would cut into their margins pretty good though so I'm not holding my breath. I find AMD's Infinity Cache approach so interesting that I'm leaning towards rewarding their innovation. It works so well while cutting costs means that their approach is probably the future for all GPUs.
Anyway, with this evidence you hopefully now have more hardware to choose from for your upgrade. I had a great luck with Nvidia for a long time (currently using Pascal), but zero good reason to be entirely at Nvidia's mercy these days. Radeons got a big bump in quality since AMD bought ATI and it'll continue to get better.