I can only comment on the Sizzix Big Shot because that is what I have. I love it. LOVE.
So far I have used Sizzix dies, Cuttlebug embossing folders, Spellbinders Nestabilities & Shapeabilities (dies) and Spellbinders Impressabilities (for embossing).
I believe the only things you can't use in the Big Shot are the Grand Nestabilities, but I'm not sure so someone jump in and correct me if I'm wrong.
I did a lot of research before getting mine -- the Cuttlebug is comparable and pretty much everyone who has one of those loves it, too.
Whatever you get--shop around. J's periodically has them on sale online, I got mine through Amazon.