If I could place the RX100 sensor in A500 for bird shooting, .........

Allan Olesen wrote:

No. The crop factor also applies to aperture.

So if you have a crop factor of 2.7 and use a 100-300 f/5.6 lens, it will behave as a 270-810 f/15 lens would on full frame.

That is:

Depth of field will be the same.

Light gathering ability will be the same.

Noise in the full picture will be the same if both sensors are of equal technology.

But:

The maximum amount of light which can be gathered will be heavily reduced, so you will not have the same dynamic range. With the small sensor it will be easier to blow out highlights.