Out of the two I prefer RedOut by a significant margin. I also marginally prefer WipEout to F-Zero, if anyone finds that helpful for calibration of taste.
FAST is faster, but the handling, tracks, AI and boost mechanics are imo poorly designed to work with one another. There's crazy rubberbanding, and the AI can collect the orbs in front of you, which are instrumental to you maintaining a high speed, and compounds the rubberbanding issue. The track designs have some needlessly punishing death traps (especially the infamous desert track, that feels like it was made for a completely different game altogether), which makes the requirement to complete entire cups without being able to retry individual races potentially very frustrating. FAST's sense of speed also relies heavily on its FOV warping as speeds increase, which is an effect I find to be rather annoying personally, and further impacts the tiny orb collecting issue.
RedOut is the slower of the two games, has a more methodical handling system to complement it, much like WipeOut does in comparison to F-Zero. RedOut actually succeeds in marrying it's handling system with its track design, and general gameplay mechanics however, whereas FAST completely fails to replicate how well F-Zero balances this. Initially, the AI in RedOut's early races was incredibly difficult, but as a response to feedback the developers seem to have tweak this to ease new players in more gradually. I'm personally not a fan of these kinds of racers containing upgrade systems (scarred by WipEout Fusion), but it's not too big a deal in this.
Honestly, I feel that FAST Racing Neo is very, very lucky that F-Zero has left such a hole in the subgenre, because I don't feel that it has the kind of quality that would allow it to be even remotely relevant in a market with a current F-Zero game. RedOut I can see standing on its own merits, even with the incoming WipEout Omega Collection. It certainly doesn't have a chance at knocking either F-Zero GX or WipEout off the pedestal (which depends on which style you prefer), but it at least earns its place to be in the running, along with older alternatives like Extreme G or Rollcage. It also doesn't make me sick in VR... which I didn't think would be possible.