General Information
While both priests and paladins have the potential to be formidable healers, there are some key differences between the two. One difference is in terms of the races available to each. For instance, a paladin can only be a Human, Draenei, Dwarf, Tauren or Blood Elf, but a priest can be a Human, Gnome, Dwarf, Troll, Night Elf, Forsaken, Draenei, Tauren, Worgen, Goblin and Blood Elf. Another main difference is inherent in the weapons available to both classes. Paladins have maces, swords, axes and polearms at their disposal while priests can mainly use daggers, maces, wands and staves.
Strengths
Priests excel in healing and damage and are extremely useful in keeping the entire raiding party alive during combat. Priests also control some of the best heals in the entire game and due to this, they're highly desirable in raids. Priests can resurrect other players who have been taken out of combat and can take on the role of damage per second. Paladins, on the other hand, are not only strong healers, but also strong characters. Due to their plate armor, they're the most survivable class in the game. They can also protect themselves and others through the use of a bubble and have the best area of effect tank in the game, holding many creatures at once.
Weaknesses
While paladins are hardy and versatile, they can also be complicated to play due to their limited mobility. They are also very specialization and gear dependent when it comes to certain abilities or spells, meaning that a paladin's talents are specific to the gear or specifications it has. Priests, on the other hand, are far more vulnerable than paladins due to their inability to wear protective armor. Priests can only ever wear cloth clothing and are thus susceptible to numerous attacks. Finally, priests depend heavily on mana for their attacks and spells, and this can also leave a priest vulnerable if mana depletes during a fight.
Combat
The choice facing a paladin in combat is whether to specialize talents. If a paladin remains a jack of all trades, it can be a flexible character, but not especially well skilled in anything. However, a paladin can specialize in a certain skill to the detriment of others, leading him to be especially talented in one area, but weak in anything else. Priests in some ways can be more versatile due to the dual specialization function. With this, a priest can both provide great damage and great healing to himself and others, leaving him a very flexible character in combat.