I love my Sizzix Big Shot Pro (comparable to the Sizzix Studio), it can take all the accuquilt dies as well as ones that Sizzix makes. It is very versatile, however, it does not fold like the Accuquilt, so if Space is an issue the Accuquilt would be then I'd go with as far as the manual machines go. These work well for doing lots of repetitive cuts for piecing. I use mine all the time for turning scraps into standard size squares, or if I'm working on a quilt that requires lots of cutting.
My partner, Dan, has one of the earlier versions of the silhouette cutting machine. Most people seem to love these because they are very versatile. They are similar to the Cricut machines, except that you can design your own patterns in addition to purchasing designs that you download from your computer. He has found it to have a very steep learning curve. I think if I were looking for something specifically to use for appliqué, I'd go with one of the electronic cutters-- people who have the Brother machine seem to like that one a lot and I've heard that it has less of a learning curve than the silhouette.
Rob