Noises and mismatch are process dependent.
In most of the CMOS P-Sub N-Well processes, pfets are placed in n-well, which has to be created in p-sub. It result with one step more with doping the silicon, so it increase variability of doping in pmosfets and thus it worse mismatch coefficient in these processes. It is not true in complementary processes (not used for years N-Sub with P-wells) or in FDSOI, where mismatch for the same transistor flavor is the same. There is an additional story in deca-nanometer CMOS related to halo implantation making mismatch coefficient dimensions and bias dependent.
Flicker noise also depends to the process. Considering CMOS P-Sub N-Well process, pmosfet is created in the n-well, and (omitting physical details) thus it channel is formed deeper than in nmosfet. So, thicker interface layer between channel and oxide results with different mechanism of flicker noise. In such processes, flicker noise in pmosfet is mostly related to fluctuation of carrier mobility and thus is lower and current density dependent (proportional to transconductance - almost constant in weak inversion and prop to square root of current in strong inversion). The channel in nmosfets is formed close to oxide (channel-oxide interface layer is thinner) and flicker noises are generated by interface traps, fluctuating carriers number and thus flicker noises are constant vs operating point and usually much higher. And again, above does not longer true for FDSOI or CMOS with N-Sub and P-Well.
In general, transconductance of both transistor types is the same for the same operating point (with accuracy to slope factor), the difference between p- and n-fets caused by differences in mobility of electrons and holes is in capacitance and thus in transit frequency.
In general, the complementary Miller Op-Amps, designed in the same process, with transistors biased in the same operating point will have almost the same performance - gain, stability, bandwidth, offset, noises and PSRR.
There is a lot of related topics on this forum showing a comparison of complementary opamps also.