The only difference is that storing one horizontal or even barrel down helps keep excess oils from soaking into the stocks on some guns. Of course you shouldn' t have a ton of oil in your barrel, but we' ve all seen older guns with darker wood around the back of the action/tang area from years of oil flowing into the wood. I have a couple of mint Winchester Model 12' s that I store barrel down for just this reason. The rest of my guns are stored barrel up. For long term storage I' ll use grease instead of oil.