I have a new to me P1500 and I do love that machine. I have had to work with finding the right thread/needle combo for Free Motion Quilting but I am getting much better on that account. I've never had a tension or bobbin issue with it.
I think the Jazz does not have the needle down position
And yes, sometimes the needle comes unthreaded. Mostly when using the thread cutter. On the good side, though, is that it leaves enough to start sewing again (if it doesn't come unthreaded).
Good luck with your decision. Let us know what you get.