1. There is no functional difference between the machines and their sizes - just as you said, how wide you can cut. I know longer have a 13" machine - I upgraded to an 18" many years ago so I don't have the dimensions. You can contact Sherri either at the 800 number or at
info@silverbulletcutters.com and she can give you the dimensions. Or perhaps someone else with a 13" can post the measurements.
We always recommend that you purchase the largest machine that you can afford and have room for. We never have customers regretting having a larger machine, but we do have those who wish they had ordered larger.
Back to the comparison between the 13" and the 15", if you are cutting 12x12 cardstock, just remember that gives you an inch spare of cutting room. The machine opening is larger, but the machine's cutting width is 13" - measured from the inside right of the machine out.
Hope that helps.
For cutting cardstock, you just need a mat that will fit the opening of your machine, and one comes with it. The super stick mat is for fabric and other materials.