The more economical route will also be more carbon-friendly.
The best way to answer the question is to drive each of the two routes for a week and compare one's gas mileage at the end of the two weeks.
Although on first impression it might seem the shorter route is more carbon friendly, we can't conclude that the shorter route is more economical -- accelerating uses more fuel than cruising, and the shorter route will require more accelerations. The energy used in these accelerations then gets wasted as frictional heat in one's brake drums when one stops at the lights.
The only way to find out is to do an experiment and actually monitor your gas usage for a while on each route. Maybe it will take more than a week, but within a month or so you should have an answer.
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