.Even if the test and project pieces are the same thickness, are they from the same side? Does the project have a glued seam that you're sewing through? Is the project piece a firmer/softer hand? Are the threads the same brand? Since it sews fine on a test piece, I'll presume the threads are the same twist.
It sounds like maybe a combination of the stiffness of the thread and the needle's interaction with the project leather. I have white, black, brown and natural (good heavens...will the spool EVER run out?) and the 'natural' color is a MUCH stiffer thread; presumably because it has a different type of, or maybe just more bonding.
When the needle starts its upward movement, the loop forms at the scarf and the hook picks it up...it sounds like the loop isn't forming correctly and maybe the hook is catching it right on the thread, resulting in tearing/cutting the thread. If your white thread is stiffer, it may be forming the loop more easily, allowing the hook to pass like it should. Double check the needle position, try a slight rotation either direction to see if it helps.