I have both - got the mini second hand from a friend (she hadn't used it much) and I bought the swing when I went back to work (school teacher). I find I get a better express of milk out of the swing - ie more milk. For me I was also quicker to express with the swing.

I can use the bottles and membrane thingy with both pumps (I still use the mini if I haven't had a chance to give the tubing a wash from the swing some days at home). I'm fairly sure that the medela bits and pieces (bottles etc) are interchangeable with the different pumps. The bottles with the swing are a little shorter and more like a bottle than rectangle-ish and long than the mini.

I'm actually glad I went with the swing in the end. (the ABA shop page had a deal going the other month - not sure if it still is - that gave a bonus carry bag and I ended up with 5 bottles and a cooler, ice brick thingy as well). It just works for me a lot easier and smoother with all the bits and pieces for me when I'm at school.