You will find that there are few rules in diving, other than the one that says you have to be on the surface before you run out of gas.
Beginning divers are often taught to do a vertical, swimming ascent. It is my belief that this is because you can execute such an ascent while remaining at all times slightly negative, which reduces the likelihood of a loss of control. However, this approach makes it somewhat difficult to stop, because to do so, you must titrate the amount of kicking you are doing precisely to how negative you are -- or, you get neutral, and if you move your fins at all (since they are below you) you will begin to move up in the water column.
Horizontal ascents, on the other hand, are executed by using breath control to move up, with the goal being never to be more than a good exhale away from neutral. This means it is quite easy to stop at any time and remain stopped, once one has control of one's breathing. It's easy to move forward and back, for example to assist a buddy (which is more difficult if you are vertical). Another advantage of a horizontal ascent is that, if you are going up a line, your fins are not aimed at the divers ascending below you!
However, when you are horizontal, it is difficult to see well what is above you. For this reason, even if I execute a horizontal ascent, I will turn vertical in the last few feet if I think there is any risk of anything being on the surface (eg. boats).
For descents, going down vertical and fins down is horrid. You can't see beneath you nearly as well as you can if you are horizontal, and your fins are aimed at whatever is on the bottom, be that silt or delicate corals. A vertical, head-down descent is favored by people who want to accelerate their downward movement (for example, when doing hot drops onto wrecks in current) but reportedly can make equalizing a bit more difficult. In most cases, I prefer a gentle horizontal drift downward, again because it allows me to stop quickly if one of us has a problem that requires a pause, like difficulty with ears, or the discovery of an equipment problem that wasn't picked up during the buddy check.