To Quest or Grind

There is only the one way to level in World of Warcraft and that is to gain more experience. Experience can be gained in two ways. From completing quests or by killing monsters of high enough level to give experience.

The only monsters that will give experience are those that are within a few levels below your current level and up. Attacking mobs more than 3 or 4 levels above you will probably be a quick trip to the local graveyard and a long run back to your corpse.

The repeated killing of experience level mobs is know as grinding. Boring? Yes, it is. Killing mobs 1 or 2 levels below you is the fastest experience. They give slightly less experience than monsters your level but the recovery time is less and they die faster

Completing quests is more interesting, although it can sometimes involve a bit amount of grinding when you are looking for rarer items. With quests you can complete errands for Non-Player Characters (NPCs). This may involve something as simple as running a message to another NPC but usually involves... well... killing mobs.

Whether you gain your experience, and thus progress to the next level, by questing or grinding really comes down to your own choice. Bored by killing? Go quest. Need a quick level for the battlefields? Go grind it out.

Since patch 2.3 quest between level 30 and level 50 give more experience. This patch also reduced the amount of xp needed for levels 20 through 50.

My personal choice is to quest whenever I can, especially since level 2.3. Actually, my first choice is to run instances in a group but it isn't always possible to find enough players for a group. The time waiting around for a group on a low population server spoils any experience advantage the group may give you.

I play Warcraft for pleasure, not to gain levels faster than anybody else.

Your choice may be different.