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Just a guess, as a lot depends on the particular car & such, but I'd say you'd be better off going for the back road. Speed up as much as you safely can before starting the steep section, and try to let momentum carry you up without needing to downshift.
I drive an Insight, and find that on some hilly sections drive often, I can get better mpg by driving fast enough to keep RPM/power up in 5th, rather than going slower and having to downshift to 3rd. Your car & road may vary, though.
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