Hey Torqs,
Your position sounds similar to my own. I completed Law last year but the two factors of not being incredibly passionate about it and the extremely tight employment market have led me elsewhere.
I have applied for both RAAF and ASA but am still currently tied up as an existing Defence member have to get processed through the lengthy transfer process. My view is that I will be happy to accept whatever comes up first, should I be fortunate to receive an offer.
I raised the question of which is the better choice with a mate of mine who currently works for ASA and he said that they have the better deal in terms of higher pay and more leave. My understanding is that the pay is similar initially but ASA employees will continue to be eligible for increases beyond most RAAF JBACs. Leave in Defence is typically 4 weeks a year as opposed to ASA's 6 weeks. That said, RAAF also has benefits through heavily subsidised housing, home loan deals, medical etc. Probably doesn't equate to the dollar value of ASA but I think they are both competitive in that aspect.
Another consideration for me is that the RAAF is a large and diverse organisation, so if one day I decide that ATC is no longer for me, there may be options available such as bouncing over to Legal in the RAAF to utilise my exisiting qualification. RAAF JBACs also have the opportunity to work in more diverse roles outside the traditional ATC such as attachment to Special Forces units. However, limitations may exist in the variety of actual ATC functions when compared to ASA.
Consideration must also be given to the terrible RAAF JBAC retention rates and what that indicates in terms of job satisfaction. People have to deal with the deployments away from home and obligations and responsibilities of military life which can be quite restrictive in comparison to ASA.
In terms of which route is quickest to attain the qualification, I don't think that's really an issue when committing to a job with the intention of establishing a long term career.