Some compounds apply more easily and more densely on the 'rough' side of leather. The bar/stick-type compounds fit that category, and sometimes they don't apply evenly to smooth leather and/or don't stick well to it. But the rough side of leather will usually scrub more compound from sticks/bars and hold it more tenaciously, without it being scraped off during stropping. You can help the application process on the smooth side, by lightly sanding the leather to give it some velvety 'nap', which will help it scrub and hold the compound more easily from the stick or bar.
Depending on what you're using the strop for, applying a heavier/denser layer of compound may or may not be best. If you're just using the strop to de-burr & lightly enhance the edge, then a very light application on the smooth side could work for that. If you're using the strop with an aggressive polishing compound for mirroring or convexing, a dense layer of compound applied to a more textured substrate (rough leather, denim, linen, canvas, etc) works faster for that. The firmer the substrate is under the compound, the more aggressive the compound will work, and the crisper the edge will be.