The Axe is hypothetically the only marker you will ever need for anything ever it is a tournament ready gun right out of the box.
Any "speedball" marker will outshoot any "milsim woodsball marker in the woods"
Their is actually no set type of gun called a "woodsball marker" what your thinking of is the tactical milsim stuff that looks like a real steel firearm
Also no marker is really more accurate than another. Marker accuracy comes down to a few different factors. How clean and well maintained your gun is and how nice the paint is. Typically more expensive paint is more uniform and rounder so it flies straighter and breaks better than cheeper paint.