I have the same problem with the sticks, my character is always moving forward. Have to pull back slightly to make them stop, it seems when the stick is idle (default position) my character still moves forward.
I have 4 PS3 controllers of varying age and wear/tear and have tried using all 4, the problem exists in every case so I don't think it has to do with wear and tear on the controllers.
Good to know this problem is widespread and it's not down to controller wear and tear.
I had this happen a couple of times with my Xbox controller. Admittedly, my console and controllers are older, but I've hardly played any games on this console at all. Never even finished a game yet. I'm a PC gamer primarily, but bought the console a few years ago just to see if I was missing anything. I've played on the Xbox more with Defiance than I've played total since I've had it. I don't think its an overuse issue with me, at the very least.
Have the same problem with the sticks, having tried it on 2 controllers. Like the OP mentioned, other games I've played recently don't have the issue so it's something with Defiance itself. Makes sniping hard for me cause I'm fighting with trying to keep my character still when lining up a shot so I'm constantly using both sticks to line up the headshot instead of just settling in a spot and just using the right (doing one of the trials, I kept walking off the platform and had to restart a few times until I got my character to stand still and remove my finger from the left analog).
Auto-Aim also seems to be random. I *KNOW* it's off but there is still some pull at times to enemies, which I've noticed with sniping as I'll be aiming for the head but get pulled towards the chest.
PSN ID: SlashZaku
Character: Amelia Lacroix