Here is how I think:

1. Homodyne needs to split the light into two branch of BPDs; ->1/2*P_signal due to 3dB coupler.

2. Heterodyne has intermediate frequency; -> 1/2*P_signal due to cos/sin IF modulation

3. Heterodyne has twice photocurrent bandwidth than homodyne; -> 2*P_shotnoise due to the double bandwidth

So I think Homodyne has 3dB better than Heterodyne coherent optical receiver. What did I miss?