PNG can only go up to 16bit, whereas .psd can go up to 32bit. Like others have said, depends on what you're rendering. Are you rendering animations? Volume effects? Smoke, fire, motion blurs? The higher-bit files take up much more space so you might not need that. A simple mask pass for example, does not need such a high bit depth. It can get confusing.
Some of the bit-depth limitation may only be noticeable in animations as dancing noise and banding that jumps around. Since you didn't post any images, maybe try the different settings and see what you think.