This is probably the most difficult question to answer since terminal ballistics are such a difficult and inexact science. There are a plethora of stories of huge deer dropping in their tracts from a well or luckily placed shot from a 22lr and then you also hear stories of relatively small deer hit with multiple rounds from very formidable and accepted deer guns and still running off to be found after a long blood trail or lost completely.
Where does the 410 rank in there? I would put the 410 slug near the bottom of the acceptable deer cartridges. I think this conclusion is fairly well support by the fact that it is such a controversial choice. If the 410 slug was well into either the acceptable or unacceptable group of cartridges the number of heated disagreements on the subject would not exist. After all my study and testing I believe the 410 slug is sufficient for deer assuming you also meet the two other area following this one.
But can we put some numbers to it, to the lethality of the 410 slug? If you read my sections on the 410 slug and testing 410 slugs you can see that most 410 slug have in excess of 700ft-lbs of kinetic energy at the muzzle. For comparison that is slightly more than most factory 357 Magnum cartridges fired from a handgun a little less than most factory 41 Remington Magnum cartridges fired from a handgun.
Although comparable in kinetic energy the 410 slug is a much different beast than either of these two well established hunting handgun calibers. The 410 slug although possessing a sizable amount of kinetic energy, it achieves this energy through the use of a light weight slug going relatively fast. A typical 357 Magnum hunting load is 158gr JHP and the 41 Remington Magnum are frequently loaded with 210 grain bullets. In comparison the 410 uses a relatively light slug ranging from about ~92gr to 114gr. So to achieve the energy it does so with a relative high velocity of 1750-1830fps, your 357mag and 41mag are both in the 1200-1300fps.
What does this mean to our terminal ballistics? It means that we have a fast light weight slug that dues to the hollow design of the drag stabilize foster slug is also a relatively fragile projectile. In my terminal ballistic testing into wet phone books the lighter Winchester and Remington slugs do fragment badly. And the one deer I have shot with Remington Sluggers the slugs was recover in relatively small pieces. This tendency to fragment means you may not get the penetration you want or need and it also mean that a hit on a large bone is very likely to greatly reduce further penetration of the lighter variety of 410 slugs. The heavier Federal and Brenneke slugs do hold up better with Brenneke slugs actually staying intact exceptionally well.
Now I have only shot a few unmodified Brenneke slugs since my primary 410 is only chamber for 2.5 inch shells and so I must modify the ammunition to make them work with my 9410 and thus they perform very differently than most 410 slugs. But even in the factory 3 inch form I would select Brenneke 410 slugs as the absolute best for muzzle energy, kinetic energy retain as they go down range, and terminal performance since they hold together much better than any other slug I have tested. I suspect this is due to their heavier weight and what I suspect is the use of a harder lead alloy than the other manufactures. That said I have to give Federal slugs a good recommendation too as they are nearly as heavy, expand very nicely but do not fragment easily and I think would leave a larger wound channel but I have no hunting evidence to support that speculation. The Brenneks on the other hand were used to take a fairly large buck and all three slugs passed clear through the deer.
But when it all comes down to it you the hunter needs to be comfortable that your chosen weapon and its ability to ethically kill your quarry. If the above has not convinced you the 410 slug is an acceptable deer cartridge than you can probably stop reading here as range and accuracy matter little if you are uncomfortable with the lethality of the 410 slug.
http://mcb-homis.com/deer9410/