Personally, (and I'm biased because it's always been my understanding that SLPs and audiologists do pretty different things) I'm not sure of the advantages of being both an AuD and an SLP. All of the speech and hearing professionals I've met so far have more than enough clients in there caseloads, no matter the setting. One area that might want to hire someone who is both an SLP and an audiologist could be a school system, because their caseloads are so enormous and public schools systems often can afford enough clinicians to go around! But I haven't seen/heard about anyone doing that.
These are super general questions and I'm sure an AuD student could help you more. First, what are you most interested in doing? Do you want to study the science of hearing and balance, assess clients with hearing and balance problems, dispense hearing aids, map cochlear implants, etc.? If so, you probably want to be an AuD.
Or are you interested learning how to evaluate and treat a whole range of speech, language, and swallowing disorders? Then become an SLP.
If you are ONLY interested aural rehabilitation/auditory training, you might be bored in a master's SLP program. Accredited MS SLP programs are required to include course work in all of the following areas:
Language Disorders
Phonology/Fluency
Motor Speech Disorders
Voice Disorders
Swallowing
Augmentative and Alternative Communication
Aural Rehabilitation
But there are definitely SLP MS programs out there that would allow you to specialize in treating Deaf/hearing impaired populations. Gallaudet comes to mind.
If you are interested in research, teaching, and obtaining a doctoral degree there are also SLP/CSD PhD programs and speech and hearing science PhD programs out there, in addition to AuD programs.
Finally, if you haven't checked it out already,
www.asha.org provides concise info about both professions.