who would win an archery contest if it was between

Tully easily! Edmure may be an incompetent, but at least he's a functional person. Lysa turned her kid into the most useless human being in Westeros.

Tully.

At least he got close to that boat, and that was a target that was much farther away AND moving, in contrast to the target that Robyn failed to hit.

If the contest was between Ramsay Bolton and anyone else, Ramsay would simply shoot his opponent directly, thus winning the contest.