If you are riding on the road a tyre requires no tread whatsoever and the less tread you have the more contact area you have with the road... treads / lugs serve to aid in traction on loose surfaces but offer no advantage on pavement and actually reduce contact area.

A narrower tyre can offer an advantage in that it will be a little lighter in weight and reducing weight at your rims is beneficial.

A wider tyre has more volume and will often resist pinch flats and there is a small aerodynamic penalty but this really only applies at much higher speeds.

The compound and casing of the tyre does more to determine it's rolling resistance and speed and there is always a plus to riding a higher volume tyre in urban environments as they can allow you to blow through things that you might want to dodge with skinnier, higher psi tyres.

I ride a vintage fixed gear bicycle that rolls on some very smooth 700:38 cross tyres and it is deceptively fast and these tyres blow through everything.

Some bicycles do best with different tyres... my stiff as nails aluminium hybrid was a pretty harsh ride on 700:28 road tyres but was the smoothest bike ever on 700:35 cross tyres which ran at a slightly lower psi.