The duel between Gandalf and Saruman never occurred in the original story. Gandalf and Saruman were both Istari, members of an Order of Wizardry sent to Middle-Earth to contest the power of Sauron. The Istari were forbidden to match Sauron's (or anyone else's) power with power. In the original story, Gandalf was imprisoned at the top of Orthanc, the tower of Isengard, presumably under escort of Saruman's guards. There was no duel.
Of course, that wouldn't have made for a good movie and the unknowing audience would have been left wondering why Gandalf wouldn't put up a fight. Rather than leaving the appearance that Gandalf is weak in courage, Jackson had to show the willingness to stand his ground, but the inability to do so.
Regarding their staves specifically, their magical powers were connected to the staves they possessed, but they were replaceable when necessary. An explanation that would fit the circumstance is that the staves were bound to the Wizards, but not the Wizards to the staves. After Gandalf escaped he enchanted/consecrated himself another causing the one in Saruman's possession to became powerless, additionally, when Gandalf returns in The Two Towers, he has yet another new staff. It is never directly addressed, but I think that the assumption that they can create their own staff when needed is a safe one.
According to the book, when Gandalf returns and confronts Saruman in Orthanc, Gandalf casts him from the Order of the Istari, and COMMANDS Saruman's staff to break, thus breaking his power. The staff is, therefore, a symbol of the Istari's RIGHT to his power and authority. Saruman could not deny Gandalf's RIGHT to a staff earlier since he had no authority to remove him from the Order. Gandalf later revokes Saruman's RIGHT to a staff, and the one in Saruman's possession immediately breaks.
I don't anticipate this being in the movie again because of the audience considerations, but instead another duel of some sort.
Purists might not like it, but it wouldn't bother me.