Quality of amps in bridged mono ?

It will change. I am not sure, but if I remember correctly either the slew rate or the damping factor changes by a factor of 2. If you run a search you will probably find the answer.

Amps can apparently be bridged in parallel or series.
This will make a difference in results......but not the fact that generally things go.....downhill.
Some, my old Rotel RB-1070, for example didn't even spec 4ohm stereo power and only listed 8 ohm bridged....apparently no 4ohm loads allowed in bridged mode.
Of course, a speaker with 8ohm 'nominal' can have some severe dips, so you really must be careful.

Running Bel Canto 200.2's in bridged mono driving Martin Logan SL3's. They are phenomenal.