I think it's a very hard question to answer. I believe Deaf, deaf, and HoH must make a united stand on this issue to ensure that we ALL get equal communication access, but I know the access needs differ for each of those groups. The hearing population is obviously by and large ignorant of our needs, so I believe a united front gives us the best chance to making progress for ourselves.
From a HoH standpoint, I am not yet fluent in ASL, so my needs focus more on the ability to read or otherwise understand spoken language. For this reason, I find captions, email, IM, etc are useful tools while interpreters are completely worthless to me. Being aware that there are differing needs in the larger group, though, I personally would rather help further the cause for all involved subgroups rather than just those that help me.
Clearly another issue we face is the huge population of deaf and HoH people who have no idea the Deaf world even exists. I fit into this category just a short time ago. The more general awareness we gain, the more chance we have in presenting a united front. I believe infighting and fragmentation of the larger group will end in less access for all of us, and the general appearance that we simply cannot decide what we want. Like it or not, I believe the hearing world sees Deaf, deaf, and HoH as a single group.