Hi there dunebug
I'm currently 38+3 and booked in at the Homerton. I was deliberating between the two and I'm very glad with my choice.
My mum had 3 complicated births at the RLH and has nothing but praise for it, so naturally she recommended it to me. Lots of my friends have given birth at the Homerton and because it is more local for me, I ultimately decided to try it.
So far, I've been absolutely delighted with the service. I see my midwife in the community, at my GP so don't have to trek down to the hospital for my appts. Midwife has been absolutely lovely.
Appointments for scans etc have been very fast- never waited more than a couple of days (gone for several growth scans now).
Apparently the aftercare in the Homerton is nothing major, but they have an amazing birth centre which I'm hoping to use, and hopefully won't have to stay in too long afterwards.
Because this is DC1 I don't have experience with either but I'm hoping the birth will be a pleasant experience there. If not, can always try RLH next time!
Good luck with your choice.