[Eomer of the Rohirrim]

Eönwë, I disagree that Gandalf's powers increased because he acquired a new staff. The restrictions set upon him came from across the Sea, not from the type of stick he held in his hand. Saruman became more powerful than Gandalf (in his dealings on Middle-earth) because he ignored the instructions given to him - not because his staff was flashier. Likewise, Gandalf became more powerful after the rules of the game changed, and he was permitted to demonstrate more power.

I'm just not sure there is any compelling evidence to say that the staffs of the Istari were a means of 'channeling' power.