Good question. The previous, but in practical terms the answer becomes "both".
Generally its a good idea to set gain for each pair individually at the start of recording, then re-adjust as appropriate during mixing.
When mixing, I always balance levels and make correction tweaks by ear anyway. That's a critical part of my post processing, even more so when mixing multiple channels, where I balance each pair separately before balancing the mix of pairs. So in that sense I'm not overly concerned with the particular level relationship between multiple channels while recording since I'm going to adjust things by ear later. From that perspective I'm setting gains so as to maximize dynamics for each channel individually while recording.
But..
Once the show gets rolling and I have the recording gains pretty much dialed in where I want them, at that point I don't want to make gain changes to individual channels because doing so would throw off whatever delicate mix balance I reach afterwards, from that particular point on in the performance. So once I dial in whatever recording gains I feel are appropriate for each channel, I link the gain controls across all recording channels so that I can adjust them all simultaneously. That way if I need to reduce levels for any one channel I adjust the gain of all of them together using one knob. I hopefully don't need to do that during any one set, but often do between sets for multiple artist acts, such as at a festival. Then whenever I do adjust gains during recording, the level change is obvious in post and I can locate and compensate for that for all channels across the board (adjusting them all by the same amount), without throwing off my mix balance.
Since I'm personally recording six or sometimes more channels, all of which are part of a multiple microphone array where each channel has a specific relationship to the others, including a tightly-correlated 3-microphone "center pair", doing this becomes even more important than it does when managing four channels.
It's sort of like the ambisonic case described above, except I don't need to precisely match identical recording gain across all channels. I only need to keep the relative gain between channels the same throughout the recording.
Keeping the relative gains the same is a practicality of mixing thing.
I'll occasionally check the lowest level channels, typically rearward facing "ambience" channels, to make sure the signal remains above the noise floor of my recording system during the quietest parts. If it does, no worries.