Schematic review: prioritized power ORing
Your schematic looks okay, but ...

An IRF7404 has a parasitic diode from Drain-to-Source, and I think you have it backwards on the schematic.  The diode will allow current to flow irrespective of the gate.

I'd probably use a BSS138P instead of that BC817.  Then you don't have to worry about bias currents or Vbe(on).