I can only speak for my Brother VQ3000, but the automatic cutter leaves thread tails that are about 3/4" long, definitely not enough to bury easily. When FMQ'ing, I pull up the bobbin thread and hand-cut them. Then all my tails are on top, easy to keep out of other quilting and easy to find when it's time to bury them.
No problem with automatic cutting--it does it inside the bobbin housing, so there's no danger to your fabric.