Your questions are difficult to answer because there are many different factors that go into residency selection. Grades, connections, performance on audtion rotations, research, and board scores are all important factors.
What do you mean exactly by a competitive residency? Do you mean Neurosurgery, Orthopedic Surgery, Derm, or
ENT? You can get match statistics for some of these programs at:
http://www.sfmatch.org/
DOs are not required to take the USMLE to apply for residencies, but for the more competitive residencies such as the ones listed above, I think it would be beneficial to take the USMLE.
Realize that there are very few DOs who even apply to the extremely competitive allopathic residencies. For instance, in 2001, there were only 36 DOs who applied for allopathic Orthopedic Surgery Residencies. For comparison, there were 882 AMGs that
applied and 217 IMGs.
http://www.aamc.org/about/progemph/eras/01stats.htm
Thus, I think it's a bunch of crap when MD students say that DOs CAN'T get into competitve MD residencies. I think that there are many US MD schools that will give you an edge, but they also give you an edge when compared to lower ranked US MD schools as well. COMP, TUCOM, and AZCOM all matched very well into California Allopathic Residencies. Connections play a large role in residency placement and if you want to stay in CA for residency, it certainly helps to go to medical school there. Also, I know many DOs from COMP, TUCOM, AZCOM, MSUCOM, NOVA, PCOM, and CCOM who did match into very competitive allopathic residencies.
The point is that you will not be limited in anyway if you decided to go to an osteopathic medical school. You will also have the added benefit of being able to apply to osteopathic residencies as well.
Obviously, you should go to the best school you can get into, but realize that the best school for you may be a DO school. You can still get into any residency you want to get into. What gets you the residency you want is
not unlike what MD applicants need as well.
Since you attend UC Berkeley, a few other random facts that you might find interesting is that the current chief resident of Neurosurgery at UC Davis is a DO. His name is Jeff Mimbs, D.O.
Check out Stanford's Cardiology department:
http://cardiology.stanford.edu/
(Click on the faculty section)
The Dermatology fellow in Melanoma at UCSF is currently a DO.
If you want to do Orthopedic Surgery, it may actually be easier to be a DO since you can apply to both DO and MD residencies. I know SEVERAL US MDs from very good schools that didn't match into Ortho or Derm. Just because you attend an allopathic school does not mean you are guaranteed a spot in any residency you want.
By the way, 40% of this year's class at TUCOM is from the UC System:
http://www.tucom.edu/admissions.htm
(Click on Admissions Information)