I use my sizzlits more frequently than my larger dies, because I like the alphas. I have found that I'm using my Sizzix less now that I have the Slice, but that's a different topic.
Anyway, I've not had any issues when I use the big red machine and the black magnetic adaptor. If the paper is thick, sometimes I have to put it through and then depress the handle a few more times than usual. I also tend to use two Sizzlits at once, putting them side by side under the black adaptor.