I find that it matters how I take the piece out from under the needle. I usually pull it, going in the direction that the thread goes through the needle, giving it a little tug first to tighten the end stitches and then pinch those stitches as I pull the piece out. Otherwise, it's easy to loosen them or enlarge the holes in the process.
I'm not a fan of the thread cutter on either machine, so wasting some thread this way seems ok to me.
hugs,
charlotte