Sorry, long detailed ramblings ahead. My conclusion is that it's a mixed bag, or: It depends. Again, my hardware is as follows:
CPU: Ryzen 7 3700X
GPU: NVIDIA 2080 Super
RAM: 32 GB DDR4 running at 3600 MHz
Headset: HP Reverb G2 running at 40% and 90 Hz
Game installed via Steam on a Samsung 860 EVO
My experience doing my usual ship stuff like bounty hunting and exploring was that I can switch from Horizons to Odyssey, even if it strains my system a bit more. In some areas EDO doesn't look as good as EDH, and I certainly miss my HUD mod setup (I've looked into the beta, but for one it has become a little too complicated for my taste, and also I really don't have the extra fps to spare for it). Some of the improvements are really nice (like the shield percentage or the SLF being shown in wing color and not just a friendly). I like the new galaxy and system map. Not sure I like the new shield effects, and I could swear the flight model has changed slightly - in EDO I keep overshooting the landing pads, and my Krait feels a little more nimble. Cockpit lighting is still a bit sketchy sometimes. But overall: Yeah, I can play that.
It gets more complicated once starports and settlements are involved. The framerate gets twitchy when I enter a starport; when I enter the hangar, and still especially when I return from the concourse and launch, the framerate gets terrible. Near surface settlements and POIs my framerate is also terrible. There is still something wrong, performance wise, at the base level.
I've done some testing today, landing and sitting on the landing pad looking at a settlement (doing a few simple fetch quest). Sitting there I get 25 to 35 fps. Terrible to fly a ship or drive the SRV. I've played around with the graphics settings (restarting the game every time I change them), and no settings "makes" or "breaks" the framerate; I lose or gain one or two, but nothing major. My GPU sits at around 80%, so there is room. Everything indicates I'm clearly CPU limited...
... Except I'm not really. I've looked at the core speeds and temperature with Ryzen Master, and examined the CPU load with Afterburner (10 ms Edit: Sorry, brain fart - 100 ms polling interval). All cores clock around 4 GHz (3.8 to 4.2), and I got no core spiking to 100% as far as I could tell (could be 100 ms is still too slow... don't know). Yet the CPU frametimes are... crap.
On foot, with the cinema screen in 3D-space, I get similar results, only even weirder. When I disembark, the framerate is crap (I get a red status display in my headset, meaning less than 45 fps) even when not looking at the settlement. After 30 seconds or so the headset's status goes cyan, meaning motion smoothing due to CPU limiting (indicating some kind of loading effect - my GPU load at the cinema screen is like 40 to 50 percent or so). Only, again, the core load is relatively low. At that point I can nose around in the settlement relatively comfortable at stable 45 motion smoothed fps. It depends a little on the settlement size and/or how many NPCs are around; the larger / the more NPCs, the more dips into the "red" I get, and in larger settlements they are more severe when turning around. This sort of "CPU limiting but nor really" state continues until I leave the settlement instance and jump to supercruse. It's similar on the concourse: Low fps due to loading cycles and then stable motion smoothed 45 fps with the headset indicating CPU limiting (the status display doesn't look at the CPU load, it looks at the frametimes, meaning: The CPU takes too long to deliver the frame).
So I'm clearly in a CPU limited state even though I should not be. The 3700X is not exactly the newest latest, but it's also not a total crap CPU, and it's not being utilized fully anyway as far as I can tell. I've read similar reports from people running 9900k's. My best guess is Odyssey is still burning CPU cycles somewhere. Probably the AI, because the few CZs I tried in VR-but-not-VR were terrible.
On the other hand empty settlements are equally bad; I did a mission to power a settlement yesterday, and the VR framerate near the settlement was equally terrible long before the scavengers arrived. I can't remember how it was on foot after killing the NPCs (I did that in VR from the ship, because I'm cheesy and bad at FPS combat).
My conclusion: I THINK I will continue in Odyssey for now. The simpler surface missions are okayish to play, and I'm not really interested in combat heavy gameplay (I did a few low CZ, but for those I switched to 2D - I got stable 60 fps with dips into the 50s on Ultra@1080p, which was okay for me). Not being able to SRV around settlements without a headache is a bummer though. At this stage I still cannot imagine Odyssey delivering the performance for full on foot VR.
Hope this wasn't too confusing and helped in any way.