Class AB or Class D for a home theater amplifier
Conceptually, a Class D amplifier is considered by some music purists to be less "perfect" in music rendition than a Class AB. This is because at the end of the day, a Class D amplifier generates digital pulses, which are then low-pass filtered to reconstruct the original sound.

However, this distinction is perhaps more a preconception than human-discernible reality. Modern Class D amplifiers like the TPA3125D2 work at high enough oscillator frequencies (300 KHz) that the low-pass filter node frequency can be well above the ability of the human ear to perceive - 60 KHz or higher frequency low-pass filters have been used in DIY audio amplifier designs.

Class AB too can suffer from distortion, especially if the load impedance is not well matched to the design, or the AB amplifier inherently has poor crossover distortion profiles. This is not so evident in "famous" Class AB chip amps such as the TDA2030 or the LM3886, both of which boast excellent Total Harmonic Distortion figures.

Also, Class AB amplifiers can conceivably exhibit distortion at lower frequencies as well, where the human ear is more sensitive to such distortion. Class D distortion is significantly at the top end of the audio band, and beyond. 

A bigger cause for concern around audible distortion in DIY audio amplifiers is power-rail voltage droop under load. While the power supply could be designed to comfortably provide sufficient current to exceed the RMS power rating of the amplifier design, the actual power requirement rises to much more than a hypothetical Sqrt(2) x RMS wattage + overhead. Even 4 x rated RMS wattage might be momentarily breached in practice, such as during big drums and cymbals clashing at once. 

If the power supply tops out in those moments, and especially if the voltage regulator's protection circuitry takes time to recover, you have harsh distortion, more discernible than any amplifier chip choice would expose you to.



There is no simple answer AFAIK, but if you are interested in personal recommendations, going with multiple Class D amplifiers has several advantages - separate amplification, pass-band and load tuning for each channel and each band, designed to align with the specific characteristics of the speakers you plan to use for each channel and band. The x.1 subwoofer / woofer amplifier can be given special attention, since it tends to be a current hungry part of the design.

The low thermal wastage i.e. lower non-utilized power overhead allows for simpler or even no heat sinking, and of course there is less load on the power supply evidently.

Knowing what actual power the 5.1 amplifier is being designed to pump out may provide better insights.