The Go baby is a die cutter machine. The die is hidden in the foam of the die block. When you layer the fabric and the pad on top, you roll it through the Go baby. The pressure as it rolls through pushes the fabric against the die blades so it can cut.
The sizzix system is the same except it was originally designed for scrapbooking. Whether the dies are interchangeable with the accuquilt system, I don't know.
The Cricut and Slice systems work in a different manner. The fabric is held tight on a sticky pad. The pad rolls through the machine. Inside the machine the cutting knife moves to cut out the shapes. It is computer driven while the others are not.
As far as I know, Cricut doesn't have the quilting specific dies like HST's, strips, etc.
There is a new Slice on the market that is being marketed for quilters. I do not know if it differs from the scrapbooking Slice. The slice is more portable, and can go cordless. It works by attaching the fabric to a sticky glass mat. You put the machine on top and the moving knife cuts out the pattern, the fabric does not go into the machine.
Hope this helps.
Price wise, low to high, is (i think) Sizzix, Go baby, Slice, Cricut.
With all you have to consider the cost of dies or with the computerized ones -cartridges and replacement knives, adhesive mats etc.