https://www.google.com/url?sa=t&sou...TSchaqaIaIQ9dUU5w&sig2=NZj8zeGEqh_H53CnLujNBA
Here's the charted outcomes of individuals that ranked programs in the ACGME match (the residency match that all US MDs go through, as well as most DOs). You might not completely understand it, but it is probably the most important thing to assess when choosing DO vs MD. MDs have a 90%+ match rate and independent applicants (DOs, IMGs, and reapplicants) have a 50%+ match rate (DOs are generally slightly higher, but still have similar numbers). There are many programs, especially in more competitive specialties, that wont even interview DOs.
Also, the reality is that the respect of the institution has a very minimal effect on matching, despite what med students will tell you. What really matters is MD vs DO/IMG, your scores, your deans letter, and for some specialties, your letters of rec.
IMO, it would be incredibly dumb to attend a DO school when you were accepted at an MD school unless you had a significant reason for doing so (wanting to do primary care is not a significant reason).