This is where the terms "open emissions system" and "closed emissions system" come from.

Open systems have a breather cap on one valve cover and the other has a PCV (Positive Crankcase Ventilation) valve. It's considered positive because crankcase air expands when heated creating positive pressure. Conversely, a negative pressure creates a vacuum.

The PCV valve is a check valve (take it out should rattle when it is shaken) that allows crankcase gases to be vacuumed out and mixed with the air-fuel mixture and burned during combustion. The breather cap is the "intake" side of the crankcase.

On a closed system, the breather cap inhales on the clean side (filtered) of the air cleaner.

If the rig is subject to emissions testing or visuals, then ya gotta replicate what it came with. Otherwise, feel free to do what ya want but as others have posted its' a good idea to evacuate the stale air and airborne particulates in the crankcase to keep the oil that much cleaner.

Oh, a clogged PCV will cause your engine to run rough because it is not receiving the volume of air vacuumed out of the crankcase... therefore, it will run rich.