I love, love , love my Cuttle bug, and also the Grand Caliber. However; I am thinking of the Big Kick, which is the new model of Big shot. because of the mover shaker dies, and the thicker dies that can't cut with the GC. I use the GC for cutting the very detailed dies, and to cut many at one time. The Big Kick is at Hobby Lobby with coupon. I did a great deal of research and this is what I have decided. Guess it depends on what you do with them., and budget.
I have never used a Cuttlebug, although I have used their products in my Big Shot. Personally, I would not trade my Big Shot for anything. It will do anything I need it to do. If you are going to be traveling with it, you might consider which machine is the lightest weight. Happy paper crafting.
I vote Big Shot. I broke a Wizard and Cuttlebug (I'm freakishly strong I guess) and the Big shot is a few years old now. Cuttlebug was only a couple months and their customer service sucked. I sent it back for repair and never got it returned, they lost it.