If you're a DO, I think you'll notice the letters a lot more, but the reality is that there are many layers of separation. Basically DO/low-tier MD vs. low mid-tier MD vs. "solid" but non-elite MD vs. Top 20. Personally I think the top 20 vs. everyone else is where the largest chasm lies. I'd sooner bet on a mid-tier school having equal MD/DO representation on the faculty than I would bet on a place like MGH/JHH/BWH picking anyone with even an upper mid-tier MD for Chief of Medicine, even if they trained at top places and published hundreds of papers afterward. Even Chief of Sections/Divisions at the Ivory Tower places are vast majority top, top-tier MD with gold-plated credentials.
I'm not sure exactly what
@83462 is asking, but there's a huge difference between "teaching" and having a tenure-track professorship. Non-titled MDs at medical schools are employees of the hospital that are often recruited for help on clerkships. Then there are a slew of "Instructor" or "Adjunct" positions that have some ties to the medical school and sometimes give lectures. Finally there are the tenure track faculty that have significantly more teaching/research responsibility and a lot more upward mobility within the medical school system. All of them teach in some capacity, but only the tenure-track faculty are legitimately vying for higher and higher promotions and more influence within the med school. The non-tenure track faculty are often paid more, because they spend more time seeing patients, but the DOs teaching at a mid-tier MD school probably aren't in positions that will lead to being Chief of Medicine or getting absorbed into the upper levels of hospital leadership.
It really is crazy. The med school admissions process is a total crapshoot, yet the school you go to can completely carry your residency application or sink it entirely. Then, even 20-30 years later, big academic or hospital appointments like Chief of [Blank] often come down to meaningless credentials like where you got your medical degree. It just looks nice to have someone at the helm without a single "ding" on the resume, just top institutions up and down.