From what little knowledge I have acquired, it seems to me that the Cricut would be better for applique shapes (endless possibilities) but that the Accuquilt is better for geometric piecing shapes (strips, triangles, etc.).
Both machines can do fusible applique shapes, but the Cricut has infinite possibilities for the shapes. Also, it seems to me the Cricut would be very handy for freezer-paper applique because you could cut one size for the fabric and a smaller size for the freezer paper. It would be worth the set-up time only for repeating shapes, though.