Both the rank insignia and the stat bars can be worn together with other accessories (including each other), but your Sim will only be able to wear one set of rank insignia at a time and one kind of stat bar at a time. This is by design, to avoid confusion.
The EA insignia isn’t this pixellated unless you zoom in close enough to feel the Sim’s breath, I promise.
Note: It is not possible to make a shoulder accessory move exactly like the Sim’s shoulders. As long as your Sim is standing still or walking, things will look fine, but if he/she starts flailing his/her arms, the rank insignia will be out of sync with the shoulder, like this:
This can be somewhat improved and I’m going to get to that eventually, but for now, this is how the rank insignia behave. The stat bars don’t have this issue, though.