Considering the regular and simple nature of the parts of the Babbage-Boole Logical Engine, one has to wonder if Babbage ever considered binary operation for his Analytical Engine.
George Boole's paper The Mathematical Analysis of Logic came out in 1847, and a copy indeed resided in Babbage's library - in which copy Babbage wrote "This is the work of a real thinker." (*) So Babbage was well aware of Boolean algebra. Nevertheless, there would have to be a very good reason for abandoning operation with numerical data in decimal form in favor of binary form.
Indeed, Babbage did at one point consider binary notation for digits. In On the Mathematical Powers of the Calculating Engine (1837), he writes about indexes to storage stored on Variable Cards, "The number of levers necessary for these purposes is not so large as might at first appear, consequently the Cards need not approach an inconvenient magnitude. For example fourteen levers and their equivalent fourteen holes will be all that is required ... for eight thousand variables." In fact, fourteen levers would be enough for 214 = 16,384 Variables, but perhaps one lever was reserved for something else, leaving 8,192 addressable Variables.
Babbage later abandoned the idea of binary representation for a certain mechanical simplicity. His later designs specified a single hole per Variable. Also, having three decimal wheels in place of (approximately) ten binary devices no doubt decided him.
Nevertheless, my argument is that it is mechanically simpler to use binary than decimal. So perhaps Babbage was simply attracted to having fewer (yet more elaborate) parts.
(*) Hyman, Anthony, Charles Babbage: Pioneer of the Computer, 1982, p. 244.