Have taken deer with both, depends on the situation. If the deer is running definitely buckshot, standing or walking slug, and distance to shots. In this case the 3" buckshot will kick worse because the 3" shell has more powder.
I started out my younger years shooting #1 Buck but back then we was huntin with dogs and the deer would most likely be haulin butt when it came by so I liked having more pellets to sling at them.Now that we stalk or still hunt our deer I have switched to OO Buck.The difference being the amount and size of the pellets.You can look on any manufacturers website and get this information and they will include velocities and differences between the 2 3/4" or 3" or 3 1/2"
Be sure to check your gun and shoot the size shells it's designed to handle.
Here is one more thought, in most states the muzzleloader is legal when ever a shotgun is. I would use a scoped muzzleloader instead of a shotgun even though I had only one shot. One shot should be all you need and as we have already debated the newer muzzleloaders can out there pretty far. A few of my friends in North Carolina use shotguns with buck shot but they are hunting in swamps and shooting at close range and you can use the buck shot to kill all the nasty snakes that are trying to kill you.
i would say try them out first to see what you like. i think a slug has a bit more kick but there both pretty close umm but id say a slug might be better becuase it drops a deer easily at close range like 50 to 100 yrds
My state is just like that. I would NEVER consider using a shotgun. Blackpowder all the way. You can shoot further and more accurately. If you are a good shot why would you consider anything else? Not trying to start something but think about it. Why shoot 4" to 6" groups when you can shoot 1" to 1 1/2" groups. Why shoot 100 yards when you can shoot 250 yards. It will open up a whole new world to you. Once again just an oppinion but I think I have made valid points. Besides I think they are more fun as well as make you a better hunter knowing there is one chance make it count.
Whitetailfever is right. If you chose a shotgun instead try to get a riffled barrel and a good quality sabot slug. They may not reach out that far but they will be the most accurate. I guess thinking about it a shotgun with a change in barrel would be more diversified. It is all in what you are looking for.