In general, a latex stain adheres properly when applied over an oil-based stain. Oil stain goes deep into the wood, leaving less stain on the surface. Therefore, the latex stain is able to stick to the wood fibers and create a smooth finish over the top.
Latex stain does not penetrate wood like an oil-based one does. If oil-based stain is placed over latex, the new stain collects on the surface and does not properly sink into the wood.
Latex stains clean up easily with soap and water. Oil stains need solvent-based cleaners. Odors do not linger when latex stains are used, and these stains dry more quickly than oils.