I have a general philosophy in life:
"?Por que no los dos?" or "All of the above"
(That is, "Why not both" or "All of the above")
I like having a buffet of options, and then I do whatever I feel like at the time. I also love the idea of there being different ways to level. I remember seeing some people try to play WoW as "true pacifists", leveling from 1 to cap without killing a single enemy anywhere ever. They used Herbalism and Mining (which give experience) and did fetch quests or "talk to people" quests, etc, that didn't require killing anyone. They also avoided dungeons/raids, even as a healer, since that would be participating in killing. While I, personally, never did it, I thought it was cool that this WAS POSSIBLE.
Sometimes I'm hyper-social and alert and want a challenge or story, so dungeons might be the way to go.
Other times, I might be in a social mood, but want to do something chill and low key, like gradually grinding out mob after mob in a camp.
Other times still, I can be in an anti-social or just "loner" mood where I want to go out and explore the map or find individual mobs to pick off in slow, solo grinds, or I want to go out and do things like gathering and crafting.
Sometimes I'm into getting story or lore for a place and want to work through some involved questchain that gives me a great story and furthers my understanding of the zone or world's lore.
About the only kind of thing I dislike are "collect 10 bear asses" quests that don't really contribute to anything and are kind of just one-offs. I don't mind chill grinding for hours - either solo or as part of a group - but :go collect 10 butts so I can...make some stew and send you on your way" is kinda...meh. Now, I make an exception here in a way: I don't mind "collect 10 bear flanks" where the flanks ARE NOT QUEST ITEMS but can be used for cooking. I remember there being some quest in WoW where you have to give the quest giver 10 of a cooking reagent, then they give you the recipe so you can cook that meal. This, to me, works with immersion, since you're actually able to make the meal itself, and it shows that the meal actually EXISTS in the game world. Somehow, that adds to immersion. There's also a chance you've already got some (or all) of the items just from killing mobs before you even got to that quest giver.
...but I'll stop there before I go into a tirade on quest design. Maybe another thread for that... ;)
Quests should be QUESTS. Incredible journeys that take you across the continent and are filled with a variety of mini-adventures. Let there be tasks that are simple and can be found (turn in gnoll/goblin ears to the guards for some faction boost + a little coin). But other than that, grinding mobs should be the primary method of leveling. Quest after quest after quest get boring after a while. Finding great groups to grind exp with is a wonderful experience.
I don't mind grinding mobs with groups but It's always better to have a goal or two inclusive to that grind other than just experience (content completion, upgrades, resources).
But I also love exploring the world too and always, always love to find things off the beaten path.