How do i tell if i need a new PSU?

Unfortunately, you would need at least a 400W PSU for a system with a GTX 960. 300W definitely isn't enough, so you'll need to upgrade. To answer your question, you would need a special device to measure the amount of power that a PSU is delivering to the GPU. As long as your GPU is functioning fine at load, then it is receiving enough power.
 
Check out the PSU Tier List HERE

CX uses lower grade capacitors, it might be alright for your system but if you can find something in your price range in either the Tier 1 or 2 list that would be better. For wattage, you wouldn't really need anything more than a decent 500w PSU.
 
Much better, for same price.

https://pcpartpicker.com/part/seasonic-power-supply-m12ii520bronze

Much better for cheaper

https://pcpartpicker.com/part/evga-power-supply-220gs0550v1

Much better, cheaper still.
https://pcpartpicker.com/part/xfx-power-supply-p1550sxxb9

Hmm, all Seasonic built psus, go figure.

Corsair CX lifespan: count on replacing before the 3yr warranty is up.
Seasonic lifespan: usually longer than your current pc, and probably the next one too. 5-7 yr warrantys, limited lifetime for XFX.

There really is no comparison.