Spent eight years in the Corps as enlisted and can't say enough good things about the experience. Of course, I didn't have a degree and only enlisted to stay out of jail (yes, I was one of "those" Marines).
A few things to consider:
Out of all of the branches, the Marine Corps maintains the lowest officer/enlisted ratio. An officer, especially a junior officer, will work his ass off in the Marine Corps, mainly because there's never enough people to go around and way too many jobs.
The physical fitness is going to be an issue. Start working on your running now. I haven't met too many O1's-O2's that aren't getting 300 on the PFT. If fact, if there's one annoying thing about every young lieutenant that I ever had, it's the fact they all ran like gazelles. The minimums won't cut it. You need to be competitive and the bar is set high.
Something I love about the Marine Corps is the emphasis they place on leading by example. As a leader, you're supposed to be capable of anything that you expect your troops to do. That includes running like the wind.
From the officers I've spoken to over the years, it is extremely competitive in OCS and TBS. They cull the ones that can't hack it pretty quick. The rest they whittle away until only the core remain. My enlisted basic class started with 130 recruits. We graduated with 74. Supposedly, OCS and TBS are even worse.
On the enlisted side, the degree won't help you much. In the army you may be able to start off as an E-4 with a degree, but in the Marine Corps that'll only get you E-2, E-3 if you're **** hot in basic training (usually only one person in an entire battalion is meritoriously promoted to E-3 in basic).
At E-4 you're a NCO. It's a serious step. They don't give that rank out without some equally serious experience.
Funny related story - I went to my MOS school in Ft. Sill Oklahoma (Artillery). They had a guy, Preston, who had had come into boot camp as a PFC (E2) and then went on recruiting duty. You can get promoted to E3 if you do a good job on recruiting duty and this guy did a good job. He picked up Lance Corporal (E3) and then went on recruiting duty again (odd, but happens). His recruiter, for whatever crack-pot reason, put in a request for him to be promoted to E-4 based on his performance at recruiting. He would have been a Corporal with less than a year in.
Our CO at Fort Sill called a formation, had Preston step up in front of everyone, and then tore the request in half in front of the entire battalion. His reason: Preston didn't even know his job (still going through school) and as a Corporal would have been expected to be better at that job than people who have spent years doing it. I felt bad for Preston at the time, but the CO had the truth of it. An E4 in Preston's job is entering firing data to send 100 pounds of high explosive downrange, often times over friendly troops and often unsupervised. There is an incredible amount of trust given to the NCO's. They have to deserve it.
Whatever standards a Marine NCO is held to, an officer is held even higher. I've met some real &$#clowns who were commissioned, but I've respected all of them for getting where they're at. You'll have senior staff enlisted helping you out and mentoring, but in the end it's your responsibility.
The Marine Corps was one of the best things that ever happened to me as a person. It wasn't always fun and really sucked some of the time, but I credit a great deal of my success in life to what I learned there.
I wish you luck whichever path you decide to take.