I just this week took my .40 Lee FCD out as an experiment. I was also running a Lee undersized sizing die, but since my brass source started shooting 4th Gen Glocks I haven't needed to, so I went back to the standard Dillon sizing die. My issue with some ammo accuracy (I think) is the cases I'm getting might be on the thick side and the FCD is undersizing the bullet, making them pattern rather than group at any kind of distance.
I never had the issue with properly jacketed bullets, though. Only plated, lead, and coated ones.