I have the cuttlebug and I love it. The dies cut thru felt like butter. It also takes many other brand of dies. I have the quickutz system too, and the dies don't really cut felt. If you run them thru the cuttlebug a few times it will cut it enough so that you will only have to snip a few spots.
From my understanding the cricut will not cut felt. It only cuts paper up to a certain weight.
I'[m originally a scrapbooker and bought the cuttlebug after doing some research. It was a cheaper machine and I didn't really have to by any adapters for other die systems because everything you need comes with the initial buy. Plus, the dies are carried at Michael's Hobby Lobby and JoAnn's. They all put out coupons so I can buy the dies cheaper.
If you have a scrapbook store anywhere close to you. Go to the store and check out the die cutters. Most stores have them on display and will let you try it out.
Here is the link for the cuttlebug. You can also find the cricut on this site. Provo Craft