I do a bit of both. If I am doing SITD I either backstitch or stitch in place, then cut the threads close (sometimes, obsessively, I'll bury the thread after stitching in place, but I won't bother knotting it then). For the tails left after FMQ I will knot and bury, and as an added precaution I will weave the end through the line of stitching (between the quilt layers). I think this helps reduce the chance of it starting to unravel, and (bonus) it hides the tail from showing through your fabric. I don't do that every time, especially if my quilted tlines are very dense.
I don't show my quilts so I am mostly concerned about appearance and longevity. Having had to unpick quilting a few times I can attest to how strongly back-stitched layers want to stay together!
Alison