For many years I used Riffe reels (vertical), but now I have been using horizontal reels (Rob Allen stainless and Aimrite) on most of my guns.
Its probably not a huge deal, but I think the horizontal reels are a bit easier to swing.
On the other hand, the vertical reels make it a lot easier to wind line back onto the reel. Gravity makes the reel hang in the proper position with no need to rotate the gun. With the horizontal reels, you have to twist the gun to get the reel into position beside the gun to wind line back on.
But that isn't as big a deal as it sounds, as I seldom wind any line back onto a reel until I, along with the fish, am back in the boat.
Just in case you have no experience with reels, you don't use one like a reel on a fishing rod to fight a fish. Its just a line storage device. When I'm trying to pull a fish up, I just do it hand over hand while swimming forward, if possible, to keep the line from gathering around me. When I get the fish in hand and subdued, I just let the gun trail behind me while I take the fish to the boat.
Of course if you are diving from shore without a boat, then that is not possible. But in that case, you get the fish in hand, brain it, string it, and then go get the gun and wind line back on.