At 52 it maths out…
Woodsman = 2.228
AP = 2.183
At 60:
Woodsman = 2.657
AP = 2.571
https://lucy.allakhazam.com/dmgbonus.html?setcookie=1
One is slower so better for casting with (100% haste on 49 delay around 25 = one Calefaction cast). It has stats. You also carry a higher damage bonus for archery shots if needed.
In practice they will be very close. Just different flavors. I kinda miss the old Woodsman tbh. Really wish ToV had a weapon with the same graphic as that or the Silver Swiftblade. VP sword withstanding.