Depends on what you are mostly going to use it for. I have a big shot and I have seen the accuquilt, they are pretty much the same thing as far as I can tell though I have not seen them side by side to do a comparison, From what I know it is the dies that are specifically designed for each.
I have used the Sizzix for appliques, it works pretty good as long as the fabric has some stiffness to it, i was using wonder under with it. I imagine starch would also work.