Assuming a 1920x1080p
Monitor, according to my findings the PS3 will display properly if the game is at 1080p and terrible at anything else. It doesn't have an upscaler (hardware or software) and it expects the TV to do that(which do have hardware scalers), except we're talking about a monitor here that expects the (PC) to do the scaling if not at all using native resolution.
It's a messy situation that arises from trying to use a single screen for all those devices.
Thankfully both the
PS4 and the
Xbox One have hardware scalers of their own, and don't expect the display device to do anything other than display 1080p.
The 360 seems to be fine too, so the only one with a problem is the PS3 and previous generations (which can probably be emulated).
I've been looking at the BenQ XL-Z series monitors,
specifically the well known XL2411Z, and concluded that it's one of the best 120/144hz monitors to eliminate motion blur in both PC and console (60hz) usage. The only unknown parameter is what happens when the PS3 outputs something other than 1080p. In that case it's up to the BenQ to scale the image and I can't find any information about that. There is a 'Smart Scale' mode, so there's some hope about this specific model at least. If anyone knows more, please share.