When I bought the Axe I used a .688 Dye UL. Then I changed to the Un1tec Lucky kit and now I use a 16" freak all american.
The UL worked well as they usually do. The Lucky was better since it's lighter than the UL and the bore was .684 through the full lenght of the barrel.
With the freak it's just amazing but much more pricey. If you can get your hands on a Un1tech lucky barrel don't heven hesitate. They are cheap but amazing. Not easy to find though...
I bought my .684, .688 and .691 kit used and for less than an used Dye Ul so I guess I was just lucky
I like this barrel so much I won't sell it even though I got the expensive full freak kit.