What type of Minecraft potions are better, drink or splash, when regarding the duration and whatnot?

Drink Potions are for yourself and usually last the same as splash potions. Splash potions can be used on multiple targets (ie. Damage or Poison potions on enemies)

Splash are generally better, specially in PVP.
Potions take time to use, but splash are almost instant, and have such a low splash range that you can easily back of and quickly use it.