These are all things I’ve gathered through hearsay and stitching bits of info together. Please take the below with a huge grain of salt. If anyone has additional/better info, feel free to add/correct where you see fit. I’m sure everyone would love to know more.
Chances of deploying:
Army > Navy > Air Force
(Chances may be highest in the Army)
HSCP:
Only the Navy offers this scholarship
Payback for specialties:
I only know how the Navy handles this... concurrent payback for “in house” residencies. Consecutive payback for civilian residencies, assuming the residency is done before HPSP payback.
AEGD:
I believe completing an AEGD is required in the Air Force and Army. I think applying for an AEGD is required in the Navy - but I do not think you are required to complete it.
Availability of scholarships:
Navy > Army > Air Force
I think the Navy and Army are roughly equal on HPSP spots (~60), while the Air Force is much more difficult to get (~15 spots?). When we consider that the Navy is the only branch to have HSCP, it seems like the winner in my mind.