Which branch of the U.S. Armed Forces has the most educational opportunities?

The USAF....we encourage everyone to pursue off-duty education....if a member (enlisted or officer) desires a Masters Degree then we will fund it. Also, long before the DoD uniform tuition assistance policy ($250 per semester hour max not to exceed $4500 per fiscal year) the USAF allowed unlimited TA.....the other services cannot say that. Oo date there are branches of the military that are ignoring DoD policy and issuing less Tuition Assistance. The USAF is the only branch of the military that has a regionally accredited community college (Community College of the Air Force). The USAF also offers great duty related and technical training.

U.S. Navy. They have every plane the Air Force has, but they can launch them from a nuclear powered carrier in the middle of the ocean. My father's education in engineering from the Navy landed him a job with G.M. that lasted 35 years.

The United States Air Force. you will love it.

DEFINITLY the USAF

USAF

US Navy. Everything the Air Force can do the Navy can too. The Navy also has the SEALs, EOD, more types of engineering than you can shake a stick at, and one thing no other armed force has; nuclear reactors.
Nuke School is tough. The attrition rate is high as most people can't handle that much education in only 24 weeks, but if you can you'll get over 3 years worth of college (~63 credits IIRC) over and done with.
Yes, you can get college credits for your in-rate training then you can add college on top of that.