I have used Carol Doaks paper, Golden Threads, and plain copy paper. I like them for different projects.
I have yet to try vellum ... but am actually on my way to the store and might pick some up.
Most of my paper piecing is with plain copy paper BUT it helps a LOT to reduce your stitch length. With a reduced stitch length, then folding the paper and creasing along the seam (or running the back of the seam ripper along the edge), I rarely have a problem removing the paper in a solid piece. The paper has a good bond to it so it doesn't tear easily in places that it is not "comprimised" (by folding or stitching) and as a result I don't have a lot of small bits in corners that I have to pull with tweezers. The draw back is that it is harder to see through, and it's rougher on needles.
I use Carol Doaks paper to make mini lone stars. You make these by placing each of the diamonds along rows on the blade of the star, each row is separated by a "blank" row. After all the pieces are placed, the "blank" row is folded so the two sewn rows meet (difficult to explain without photo's). Using heavy copy paper can't give me a tight enough fold and without a tight fold, you lose your points in between each diamond of the blade ... not to mention getting all 8 blades to fit when you're done. So for these I use Carol Doaks paper. This paper is to me more difficult to remove because it tears so easy that I end up with tiny corner bits everywhere that have to be removed with tweezers.
My favorite paper by far is golden threads tracing paper. It has a good bond so doesn't tear where you don't want it to tear (ie no little bits stuck in the corners - but again I use a small stitch) and has great transparency to help with placement. However ... I have not yet succeeded at getting this stuff to feed through either an ink jet or a laser printer. I have to print the block onto regular copy paper, then trace the image onto the golden threads paper. I'll do this if I only have one or two of the same block to trace, but not multiples of the same block (my lone stars would NEVER match if I had to trace 8 blocks).