Not sure I fully answered yesterday when I listed high-gloss painted and high-gloss urethane or varnish as equal, they actually are not quite equal. A varnish (used only on high-end finishes these days) or urethane (latter is more resistant to wear and easier to apply) will clean nicer than most paints, but are commonly more subject to staining or etching by oily dirt because they are oil based. A latex (usually acrylic latex or latex enamel for kitchen use) will generally clean up a bit easier with oily dirt (like cooking oil) but is more prone to gradual wear-through from repetitive cleaning and generally show streaking more from cleaning, and usually a LOT more prone to fingernail damage if you do not have knobs on the drawers and doors - commonly fairly quickly show bare spots from the wear of grabbing the same spot to open time and again.
Also, obviously, a stained finish needs a clearcoat over it for protection - otherwise it will pick up stains (especially oil stains) VERY quickly. Course, over wood most paints need a primer under them and commonly two coats on kitchen cabinets to give a durable finish, so that is three (or more if spraying) coats.
Paint is easier to touch-up to match because it fully covers - stained surfaces get oil (commonly finger oil) ingrained into the damaged surface, so restaining gives a mismatched tone - generally darker - at the damaged spot. Even if you get the oil out, restaining a damaged area commonly takes a light touch with a rag or Q-tip or such to get just enough stain to match (commonly several passes) because a full-penetrating wipe will normally come up darker than the original coating - much darker if the area was sanded or solvent-cleaned and originally had a sanding-sealer or sealer on it.
