Ok guys

The manual of the VPI HW-19 MKIII recommends that "the dust cover be down when playing records. Under most circumstances this will result in cleaner sound since the cover acts as a 'shield' against acoustic feedback." And of course keep the record and stylus clean. 

Put. me in the cover on camp. SQ better.

What brand ,model turntable and cartridge ? How good it is will have a lot to do with its stability and vibration control.  I don’t know of many quality turntables with a built in lid.

This discussion illustrates beautifully the problem with technical attributes. The subject at hand is dust covers. But it could just as easily be amplifier watts (is it better to have more or less?), speaker cables (is it better to have silver or copper?), or any of a hundred other technical items. 

Everybody wants a simple answer when the truth is there are no simple answers. Its better off, probably, unless its a table designed to be better with it on and down, in which case it should probably be on and down. Probably. The only thing we know for sure is which way it sounds better determines which way it goes- and not the other way around. So once again might as well just cut out the middle man. Go and listen. You will see.

It's good to have a dust cover to keep your table clean when not in use.  When using, do some blinded tests and see which you prefer.  If you can't tell the difference, then play records without cover so you don't have to bother with it when changing sides.