The vast majority of Muslims are Sunni, but that does not explain why we have had a close relationship with many Sunnis nations. I think the main reason we have tried hard to work with, for example, Saudi Arabia, is the obvious reason - oil.
Sunnis throughout history have been aggresors and slaughterers of infidels. Shias have, because they were persecuted by Sunnis, been less likely to do this and have syncreticism in their nature
Shia Iran has Christian and Jewish communities who can worship and have their own places of worship with little abuse
Sunni states on the other hand, with the exception of Malaysia and Indonesia (to some.. extent) do not allow any of this
Sunnis are basically "the Koran is the literal truth" and the Koran is nasty about infidels. Shias have interpreters so some (like the Ismailis) are actually against violent jihad etc. -- because that was pronounced by the leader and is binding on the future.