Chances are, that it is similar to oblivion, with the Dragons being Gates, and you go about the main quest and only need to kill a selected few dragons for quest reasons, the dragon shout would be like a sigil stone (reward for closing oblivion gate) in that you can avoid them and just do the main quest.
I to see dragon shouts as much the same for spells as sigil stones was for enchanting.
However dragons are random encounters, you can probably avoid many of them but also want to kill them for the shouts. Wonder if I also can soultrap
Now to kill dragons, they are creatures like everything else, they are not like Dagoth Ur who require a special way to kill. Do enough damage and they dies, they are boss enemies so they have lots of health and also strength and weaknesses, they might have location damage but if so they would have even more health.
Stealth and bows should work very well as they are large and easy to hit, poison might work, however they might be immune or cast cure poison as it's a obvious way to kill them. Probably immune to paralyze as it would be to easy.
One strategy I will try out is to try to find a place with some cover, a ruin would be ideal as it would have small openings where the big dragon has problems getting, now you can do ranged attacks. Now the dragon can respond with ranged area effect but I will be far safer from other attacks.
One last thing, dragons will be level scaled or area scaled, as they are random encounters and you will face them from early in the game they has to have some levelling. It is also confirmed that it's many types who are different, this might be the different levels of dragons.
I also have a feeling the dragons are hunting you so you run into far more dragons than others.