While Favored Foe is also concentration, it doesn't compete as hard (except for with ensnaring strike unfortunately) with these spells, you can shoot your lightning arrow, get the effect AND mark the target with the favored foe all in the same turn. Even with concentration free hunter's mark you can't do that.

Does favored foe take concentration?

You can't concentrate on both a D&D spell and Favored Foe at the same time. Whether you're concentrating on a spell or something else that requires concentration (as if it were spell), you can concentrate on only one thing at a time.

Can favored foe stack with Hunter's Mark?

I'm curious, can you stack Favored Foe and Hunter's Mark together? No, since you can't concentrate on both at the same time.