Yes, the degrees are truly equal, not like the MD/DO thing. DDS/DMDs do the same exact procedures as dentists, belong to the same ADA, and apply for and train in the same residencies and specialties. There are no "DDS only" or "DMD only" residencies as there can be in medicine (DO-only or MD-only). A friend of mine here in dental school will graduate with a DDS and go to work for his father who attended a different dental school and has a DMD.
It is merely a historical difference between the two and just depends on which degree your dental school awards. Back in the day, some schools thought they'd give DMD, some decided on DDS. Since they mean the same thing now, the schools have just kept the difference going as a historical thing.
There is absolutely no difference in prestige either (as you allude to with the MD/DO thing).
So based on that, listen to what doctorsquared said and pick your school based on the curriciulm/students/clinic, etc, not on if it gives a DDS or DMD.