Comparing your set back and stem numbers from both fitters, I'm a little floored that the total reach difference of 3cm with about the same bar drop. Didn't one of those feel cramped or too stretched out?
Also, the second fit has less knee bend angle, yet a lower saddle, which is illogical. Was he measuring your knee bend with your heel dropped, or the other guy with you toes pointed down? Based on your cycling inseam (you have longish legs, BTW), the 73.5 saddle height sounds closer to ideal based on the .883 method.
Finally, the difference in effective TT length is 1cm, adjusted for STA. Given that, why does the second guy have a 2cm difference in stems between M and S? It should be a 1cm difference to counter the 1cm ETT difference.
Overall, the first fit seems closer to correct, and I think the second guy has you sitting too low, which makes the stem come down to where it has few or no spacers. I think that is why the second guy thinks M is too big - no spacers. Meanwhile the first guy has you needing almost the max spacers for the S, which is why he probably favors the M. I think the second guy is just messy in his knee angle measurements, which is how you ended up so low. He's also messy with other math. I don't know who is right about your reach, since those numbers are wildly different as well.
I think you can ride either bike fine. You won't need an 80 stem - 90mm at the shortest for the M. Pick the one you think will look best with spacers and stem length. I would favor using the first guy's fit numbers, either way. You can certainly play with set back and stem length without needing a different frame, so there isn't a lot of risk.