To test this you will want to complete a R to L strength test. Pretty simple, but often overlooked. Here’s some issues that present itself when there is a weakness or a discrepancy:
One shoulder collapses with speed/OLY lifts (specifically jerk and snatch).
One shoulder fatigues faster than the other, thus limiting performance overhead.
You punch your head through the window excessively to try to compensate for weak positions.
You can’t HSPU.
You have pain with fast lifts, but not strict lifts overhead.
You’ve developed an overtraining injury on one side that is hampering you ability to perform.
Try this test out: find a weight you can do at least 5 reps with, no more than 12 (ideally) and perform a max set on each side once that load is established. Should be slower down than up tempo, no hips!
Don’t guess what is holding you back, take the test and get to work!