Everything now is speculation so it's hard to give advice. We will need to see how residencies adapt to the changes, and the students (and schools) will change accordingly. Alumni network and past results (e.g., residencies who had good experiences with graduates from certain DO schools) may help. Schools with a large clinical rotation network, and their own large residency (medical school based osteopathic residency network - OPTI) can help.
Examples of OPTI - PCOM Med-Net (32 residencies, 1200 spots)
Graduate Medical Education (GME)’s mission is to develop qualified, competent and caring physicians in the ambulatory, hospital and extended care settings.
www.pcom.edu
Someone brought up research. Compare to MD counterparts (with a few MD school exceptions), DO schools are not even on the radar when it comes to clinical or bench research. The older schools do conduct some research, but no where near the level of MD schools (which mostly are attached to major research universities). However, if your DO school is located near major research universities (ie PCOM in Philly, Rowan in NJ with Rutgers in NJ or the universities in Philly across the river, NYIT and all the schools in NYC, CCOM and Chicago, etc), there are opportunities for eager students to find researchers (quid pro quo - I'll do free lab labor, you get me published, maybe make connections with your clinical friends). If you're in Gaylord, MN studying medicine in a renovated elementary school building - good luck finding research nearby - it's a 2 hr drive to get to Mayo Clinic in Rochester, MN.
Now some of the newer MD schools are similar in style to DO schools, and may run into similar problems.