Personally I'd be more comfortable with KEMH purely because after I had a car accident while pregnant with DD2, I stayed there and they looked after me so well. I felt comfortable knowing I was in a facility that could handle anything that might happen rather than having to be transferred mid-emergency, iykwim.
But if the Doctors are happy for you to be in either hospy, then of course you will be more comfy in a private one. You'll get your own room (bit lonely tho?), better food, prettier room, etc.
I'd still stay with KEMH, but that is purely because I'm so loyal to our public health system! I think we have some of the best maternity and neonatal services and facilities in the world
Good luck making your decision. I hope all goes well for you and bubba over the coming weeks