At this point, it's impossible to say, I don't think we even have much detail on finishing moves beyond that they exist. Are finishing moves special attacks you can perform (Though presumably only when specific conditions are fulfilled as "finishing moves" implies that they always result in the death of the character you're attacking, thus making them one hit kills, if they're a special attack, so if you can perform them whenever you like, it would basically allow you to one hit kill all enemies.), or will they simply be special animations that are sometimes shown when NPCs die? Hopefully, though, finishing moves can be made to look good in both first and third person either way. I don't want the game to make a sudden transition into third person when finishing moves are performed as that could get awkward, or if it is used it should be an option you can toggle like the cinematic kill camera in real time gameplay in New Vegas. If I CHOOSE to play the game in first person, I don't want the game forcing me into third person against my will, the more the game can cut down on things like that, the better. If it's an option, though, that's fine because then I only have to get it if I want to.
I was actually thinking about this, but finishing moves really aren't new to Bethesda. They were used extensively when using VATS in Fallout 3 and New Vegas (Obsidian). One of the only reasons I liked using VATS was for finishing moves, when the camera would zoom in on the side of the player's face, and then follow bullet/laser/etc. burst from the weapon and impact the NPC. I can definitely see Bethesda making full use of that with bows and arrows, and it would be interesting to see what they do with magic.
I wouldn't quite call what we got in VATS finishing moves as that implies that your character actually does a special animation for finishing off an opponent, but in VATS, you really didn't get that, the camera just moved to dramatic angles and you got cinematic tricks like slow motion and the popular "following the bullet" camera. If finishing moves exist for ranged combat as well, I could see us seeing something similar to using VATS with guns, except of course with bows and arrows instead of guns and bullets. But for melee, VATS isn't really like what I expect finishing moves in Skyrim to be.