Guild Wars 2 has no quest log, outside of the Personal Story questlines, which are more of a solo endeavor (though you're totally able to group up for those if you choose). That alone should say how different it is from the normal 'collect quests, do quests, turn in quests' concept.
Even though the content of events themselves is somewhat standard in its execution (to a degree - one of the best things about events is that there are often quite a few ways you can progress towards completing them), not having a quest log is... strangely liberating. Events pop up all over the place, with different events happening at different times, many dependent on the stage or completion-factor of other nearby events... it's very, very easy to get distracted in GW2.
If it's similar to Skyrim in any way though, it's that you're deeply rewarded for exploring. In Skyrim, choosing to hoof it all the way across the wilderness and letting yourself get distracted by every single thing along the way (of which there is plenty!) is very rewarding, and GW2 is the same way in that you're rewarded for letting yourself succumb to the lure of wandering aimlessly.