I prefer horizontal STG games, because I like not only to dodge bullets, but also immovable grounds, floors and ceilings around my ship, which you won't find often in vertical STGs. They allow the designers to create a more compelling world around your avatar, too, with a thick atmosphere. Horizontals are also more varied in my opinion, like when they offer portions of vertical scrolling as well, without changing the horizontal orientation of your ship/character. For example in the 3rd stage of R-Type III or partly in every stage of Andro Dunos.
Verticals are usually strictly one-way with no immovable obstacles, a variation may be ground targets, like introduced by Xevious, later refined in Layer Section, it's not often used, though. The catch in Verticals is mostly a complex scoring system, intriguing game play elements like in Silvergun, Ikaruga and ASOII or your huge room to move, while dodging bullets of different speed. It's called "depth" but more often than not it's just distracting and forces you to concentrate on a system rather than an immersive world. It's rewarding to get into such a system, but it's probably not the kind of reward I look for in a game.
Side note: It may sound strange at first, because it's the same genre, but not only there's a huge difference coming with direction in an STG, it's also very dividing for players. There are kind of crossover titles like Progear or Sengoku Ace, which can count as a try to transfer a vertical STG into a horizontal orientation, or conversely games like Image Fight or Formation Armed F apply horizontal characteristics within a vertical environment. Well, maybe the best of both worlds are axonometric games like Zaxxon, Viewpoint and Under Defeat.
