I have the Big Shot - Use this a lot with sizzix ,cuttlebug and any other steel die to cut felt always use wool blend felt as it makes a cleaner cut.
Craft Robo- Love this and there are loads of free designs out there for this machine but it wont cut thick card very well and I dont think it will cut felt.
KlickNKut this cut thicker material and also felt, only just realise this so i will have to have a go
again lots of free designs.
For Robo & KlickNKut try http://www.scrapmag.info/crafty/index.php?cat=0
It is in French but easy to navigate.