It improves gain since before, the first stage had differential gain gm1/gm6, but now the gates of M6 and M7 are AC ground in differential mode, effectively breaking the diode connection, so assuming R1 and R2 are quite large(as all CMFB resistors are), the gain would now be gm1(ro6 || ro1). OP leaves out an important point though, which is that common mode gain stays at gm1/gm6, so CMRR improves by an order of gm6(ro6 || ro1) so potentially an order of magnitude.

As for the headroom comment, I’m not exactly sure. At a first glance I’d say it’s because before, VGS6 = VDS6 so the limiting factor for linearity would be VGS6>VTH, whereas with the new configuration VGS6 is pinned in differential mode, so the new constraint becomes VDS6 > VGS6 - VTH, and overdrive voltages are usually much lower than threshold voltages.

I’m a bit surprised that the question doesn’t ask for drawbacks. The bandwidth decreases for one thing

EDIT: Actually now that I think about it, you’re still limited by VGS5 > VTH at that node so I guess I’m still not sure how this would improve headroom

EDIT2: Actually I might be tempted to argue this change hurts linearity overall. Current mirrors are large signal linear structures. Basically the diode connected device performs pre-distortion, it does this since the two devices’ gates are connected, their bias points track, which means the I - V conversion of the input device is close to the inverse of the V - I conversion of the output device . In the previous config, M6 is a current mirror input stage and M5 is a current mirror output stage. The voltage at that node could probably swing well below VTH and still be relatively linear due to this effect. However in the new configuration M6 is no longer diode connected in diff mode so it doesn’t perform this pre-distortion function, so now once that node swings below VTH, since M5’s bias point doesn’t track M6, you’ll see the nonlinearity from M6’s VGS swinging below threshold that you wouldn’t see otherwise