I personally prefer using the June Tailor Shape Cut for cutting strips.
With the Accuquilt, what I don't like is that the strips develop a ripple (from the fabric stretching under the rollers) about halfway through so I have to lift up the mat and pull the fabric once or twice. If I don't do that, a ripple gets pressed into the strips which also makes the edges in that area uneven. Also, I don't like the pre-cutting I have to do with the Accuquilt in order to be sure I am not wasteful of the fabric.
For me, it's actually quicker and easier to use the Shape Cut.