The Stelvin screwcap bottle system is best layed down as the bottle cap has an oxygen permeable membrane. The porous barrier of the screwcap acts as a cork does and allows for a minute transfer of gasses. The degree of permeability of the cap depends on the manufacturer. Grégory Patriat, Jean-Claude Boisset’s winemaker, who bottles under natural cork and screwcap, prefers to store screw capped bottles lying down in order to have a good exchange between liquid and the air through the seal. Wine that is to be drunk within a short time frame, such as 12 months, will not benefit significantly from storage either vertically or horizontally.
If your wine is to be cellared for a longer period then lying down is preferable.