There's a difference, Chakotay MAJORED in Anthropology. Picard took some class presumably to fulfill graduation requirements but took a liking to the topic.
We have every reason to believe Picard took the shortest route to command, which in the Star Trek world generally seems to be taking that route through the Conn position. We know he has an extensive pilot background that might even rival Riker's and maybe even Tom's.
Chakotay appearently majored in something more than Anthropology. This is from Memory Alpha.
Chakotay possessed great piloting skills and during his first year he trained as a pilot in North America. He then went to Venus for a couple of months to learn how to handle atmospheric storms and later dodged asteroids for a semester in the Sol system asteroid belt. (VOY: "Future's End, Part II")
He resigned from his position as an instructor in Starfleet's Advanced Tactical Training and sometime later joined the Maquis. (VOY: "In the Flesh")
I know I read an article some time ago in the now defunct Star Trek Magazine
about Chakotay's bad luck with shuttles (and yes it's not a good record) but the worse record belongs to Tuvok and he didn't even have to be piloting, all he had to do was be along for the ride to have the shuttle crash.