The East, while never denying the seniority of the Roman bishop in the patriarchal τάξις of the early Church, has nonetheless objected to certain innovations in the modus operandi of the papacy, especially in recent history--i.e., from 1870 onward. Since the 19th century, particularly in the papacy of Leo XIII (1878-1903), we see papal roles change dramatically with the loss of the Papal States and the rise of the pope as "global teacher" whose writings begin to increase in number and scope alongside his increasingly well-financed claims to authority, most egregiously (and ecumenically intolerably) manifested in the claim (in the 1917 Pio-Benedictine code of canon law) that the pope is the one who appoints all the world's bishops. This is so startling an innovation, so unprecedented a claim (until the end of the nineteenth century the popes were not even appointing all the bishops on the Italian peninsula--never mind the rest of the world), so wholly without theological justification, that Eamon Duffy, author of the best one-volume papal history Saints and Sinners rightly called it a "coup d'Église." This idea that one man appoints all the other bishops will never fly in the East.
Now a new volume out from Cambridge looks at other transformations, focusing, in the main, on individual popes from Julius II onward. This is not a comprehensive history like Duffy's, but still looks fascinating.
James Corkery and Thomas Worster, eds., The Papacy Since 1500: from Italian Prince to Universal Pastor (Cambridge UP, 2010), 286pp.
Going back even farther, into the latter part of the first millennium, we have another new work out from Cambridge:
Caroline Goodson, The Rome of Pope Paschal I: Papal Power, Urban Renovation, Church Rebuilding and Relic Translation, 817–824 (CUP, 2010), 408pp. + maps + illustrations.
Goodson's book looks to be a continuation of the arguments first begun by Pope Leo the Great, and analyzed by Susan Wessel: viz., the project of rebuilding (in Paschal's case quite literally) a "spiritual" Rome to recover "universal" respect and allegiance after the transfer of the capital to Constantinople and the collapse of the empire in the West.