I was in the same boat, between MAMS and MSMP. Talked to students from both programs about them (some of which are currently at Stritch). The main two things lacking in my application are clinical volunteering hours and undergraduate science GPA. From that standpoint, doing well in a science masters in either medical science or physiology would prove that i can handle the rigors of a graduate-level science education. So that covers academics. The other thing is clinical volunteering. It seems like MAMS structures it's curriculum specifically (only Tu/Th classes) so you can add to your clinical volunteering hour amount. The students who were former MAMS alumni volunteered at Lurie's Children Hospital, free health clinics etc. And they said these locations keep spots open specifically for MAMS students. On the other hand, with MSMP, because it is at the Maywood campus (outside of Chicago), you are competing with medical students for volunteering spots and because of the set-up of the MSMP curriculum, it's less likely that you will be able to commit more time for clinical volunteering. MAMS also offers a committee letter at the end of the program, which MD/DO schools look at very favorably. The final case for MAMS over MSMP was location; MAMS is located on Loyola's undergraduate campus (Lakeshore), while MSMP is located at the Maywood campus (outside of Chicago). I did my undergrad at a school in proximity of Loyola and loved my time there, so that was another plus. But I factored in location after looking at how each program could suit my needs for upping clinical volunteering and proving my abilities to succeed academically.
I don't want to sound completely biased towards MAMS. The staff at MSMP (especially Dr. Pak who interviewed me) were super nice and very helpful, giving me general advice on the whole application process. When I talked to Dr. Pak, she stressed how each student (since it is a 30-35 person class) is given multiple advisors who are always keeping tabs on how each student is doing academically. So there's no way you can get lost as a SMP student, which might happen at some of the East Coast-based SMPs that I looked at. MAMS is about 50 people/class, which is a slightly larger cohort (fyi). But what I've gathered from students at both programs is they love the Loyola style of teaching and are either happy at Stritch or are hoping to matriculate this year. Also, the Guaranteed Interview (3.6 GPA+) is also a draw for either MSMP or MAMS and the stats for that is about the same (around high 90%s). I think that was it for now, feel free to PM me if you have any other questions.
Also Dr. Franks (MAMS director) hosted a webinar (link is somewhere on Facebook), where she details the whole program, if you are interested.