The Shi'a caliphs would probably have more temporal power as Shi'ism has an exstensive and organized clergy, so I guess he would be more similar to the Pope than his Sunni counterpart.
There would be no Shi'ite caliph! The only caliph that the Shi'ites accept is Ali (the fourth caliph) whom they consider the only rightful successor of Muhammad.
Except that there WAS !
Fatimids were Shiite Caliphs, for a token of fact. The Shiites believe that it is only Ali and his descendants, that can be the rightful Caliph.
1) That would be difficult, given the currently to severely incohesive political composition of global muslim community.
2) On the one hand, a Sunni "caliph" would be a sort of spiritual figurehead, like the Pope in Rome. However, the caliph would have less control over temporal matters than the pope due to the lack of a hierarchical clergy in Sunni Islam.
3) The Shi'a caliphs would probably have more temporal power as Shi'ism has an exstensive and organized clergy, so I guess he would be more similar to the Pope than his Sunni counterpart.
In regard for the Sunni/shia divide, I've always imagine the Christian analogue would be, had Jesus and Mary Magdalene had offspring (damn you, Dan Brown!), the Christian analogue of Shi'ites would argue that only these descendants could ever become pope...
In regard for the Ottomans, I was always under the impression that when it was in regard for caliphal power, the Ottomans were more "in name only" than exerting actual power beyond their own territories. Yes, I know of stories about how the Muslims in Southeast Asia or West Africa included the Ottoman sultan in their prayers, but the sultan didn't excert any direct influence there. Of course, there's a crucial different between Islam in Ottoman and modern days compared to those of the early caliphs, namely that today the vast majority of Muslims aren't Arabs, and that because of this, the early Caliphate enjoyed a much greater cohesion.
Hmmm.... btw, I've been wondering in regard for the original premise of the thread: namely a Caliphate by 2009. The options are either having the last one (ie, the Ottoman sultans) continue, which requires a very different Turkey post-WWI, or a restored Caliphate. The latter I find very difficult in the environment of the 20th century, though.