As mentioned in the comments, the Dragons in the game were originally meant to have the Unrelenting Force shout as a power, but this was removed in favour of only being able to use more "traditional" powers - the "breath" shouts.
A theory for this can be developed by looking at the storyline.
When the player reads the Elder scroll, he is teleported back in time to the end of the Dragon War, when Alduin was "Defeated". This led to The eventual defeat of all Dragons (save Paarthurnax). However, Alduin was not defeated, he was simply pushed through time, to the present day.
When he arrives, he is capable of summoning forth meteor storms, and even raising the dead - this is because from his perspective, he only "vanished" for a short period of time - he is still at the height of his power. The other Dragons, however, have been dead for centuries.
Dragons are believed to have a close affinity to magic. But, if left dead for long periods of time, it would make sense that much of their power has left them, and needs to be restored. It would then make sense why a handful of mere mortals would be able to kill one on a simple reconnaissance mission.
This is further supported by the idea that while dragons fighting could be described as a "heated debate", but I would argue that there would have to be some form of residual power involved in using a Thu'um - otherwise that Dragonborn would likely be killing a lot more people simply by sneezing violently.
So, my belief is that Dragons require some level of affinity with Magic to be able to use the Thu'um to it's full effect, which does require time, and training.