Yes, there is more responsibility. How the run goes depends much more on the tank than on the others, I noticed it when playing WHM.
When you are the tank, with experience you notice the quality of the group makes a lot of difference, but except notorious cases, you can't spot that easily (as a tank, you are too busy usually, healers spot things much easier) who is saving the day or making things harder. A healer can DPS and many DPS can heal, so they can fill holes if necessary.
But when you are not the tank, you see how the tank affects the run. A bad tank makes the run messy, a good tank that does not know well the map may have you making tours of the dungeon or simply goes slow, one who is good but goes too quick makes the run more stressful, etc.
Tanks mistakes are there for all to see, much more than other roles. You are expected to know everything (unless it is new content and nobody knows, that is so much more fun.) Most people are very nice and helpful, but some are not, usually the ones who don't play well.
If you find it is boring or easy when you do a dungeon for the nth time: Farming and grinding and doing a dungeon n times is boring. I can't see how doing a dungeon n times as a DPS will be more fun. The first two or three (or maybe more) times you tank a dungeon it won't be so easy or boring.
I don't know in Coil or Extremes where all roles have to know the fight very well and do their parts and coordinate well, and Titan HM I think is easier as a tank, on the rest of places it is more stressful. There are places where healing is stressful too, but only certain places, and not in the easy dungeons. When you play other roles, one of the risks you take is how will the tank be.
