I can speak to general surgery. Reality is that there are only ~3-4 former AOA programs that are even on the same level as MD community programs. The volume and variety just isn't there. Even for the better DO programs it is a lot of bread and butter and much less of the complex Onc, Vascular, and advanced GI you see at even the MD community programs. Additionally, DO programs do a LOT more endoscopy in their surgery residencies than MD programs do. Fellowship opportunities at former DO programs are also more restricted. To put it in perspective the residency my DO school was affiliated with had less than 10 actual faculty. The regional academic MD program I am a resident at has the same number in a single department, with all surgical departments represented with multiple faculty in each specialty.
Academic job opportunities are limited coming from DO GS programs, and community jobs can vary quite a bit regarding how much of a problem it is. Large employers looking for a cog in the wheel don't really care where someone trained, but the private groups are often more selective. Even then it really comes down to case logs, what the group is looking for, and other factors (like are you from the area and are more likely to stay long term).
There are differences in the surgical subs as well, although they can be different than in GS. Most of the DO surgical sub programs rotate at a lot more hospitals than the MD programs do. Unfortunately it doesn't matter what the differences are in job prospects and training for DOs in the surgical subs because the decision to go to a DO school significantly impedes even the idea of matching a surgical sub at an MD program. Just be grateful to have matched and make the most of it.
Research opportunities really aren't comparable so its not even worth commenting on.