What a great question. My perspective is from being a DM. This was a game with PC dragons (metallic). I found I had to adjust substantially for the shapechanging abilities. This was unexpected - what I was more prepared for was (for example) the players being a very desirable target for the local nobility. Dragonslaying was all the rage in the land where they started out their adventures. All the various parts of a dragon were worth a fortune to all sorts of different magic users and craftspeople, and therefore dragons were hunted and poached.
However, the ability to shapeshift three times a day for free became much more of a challenge for me than almost anything else. I had to make much more of an effort to "populate" their world with the right sort of encounters, since they had a lot more flexibility in terms of form and special abilities. It certainly made me up my game!
The best dragon characters in the party were the ones that had a substantial "break" with their home culture, but also kept the alien and magical nature of the dragon, instead of simply "playing a human in dragon clothing".
Since they are so long-lived, it's easy to see that they would be much more risk-averse than humans. They have more to lose, in terms of years of future. Time moves much more slowly for a dragon, unless of course, there is a reason they're in a hurry to adventure.
One of the PCs in the party had a dragon disease that was terminal, and had to find certain substances in order to take back to their tribe for a cure. Another was cast out solely due to a mistaken divination. The dragon had to find proof of the interference in the divination, and then get the proof back to their family, in order to be restored to their position in the hierarchy. The others were motivated by a love of money, in one form or another.