I think your major difference is time.
An accredited bachelors in teaching is a 4 year degree (Usually 3 years plus an honours year).
From what I can find, most graduate diplomas/masters for teaching are 1.5 to 2 years full time. Assuming you completed a standard 3 year degree, that means it's 4.5-5 years before you qualify to teach.
In your case, you'd be looking at:
Bachelor of Science/Bachelor of Law - 5 years full time
Bachelor of Science/Bachelor of Education (Secondary) - 4 years full time
If you decided to take on a post grad teaching qualification with the combined law degree, that's a minimum of 6.5 years before you qualify as a teacher.
Also, there is no guarantees that you would be accepted into a post graduate course. These have harder requirements, and it's impossible to predict how you will perform at uni. Fees are generally higher.
Comparing the Bachelor of Education (
http://handbook.mq.edu.au/2017/DegreesDiplomas/Degree/Bachelor+of+Education+(Secondary)) with the Masters of Education (
http://handbook.mq.edu.au/2017/DegreesDiplomas/PGDegree/Master+of+Education) , to me it looks like the Bachelors course is more comprehensive and is designed to give you knowledge in many areas. The masters course (which I'm using as the Grad Dip equivalent) is similar, but because you'd already have a degree, you don't get to cover broad areas (like History and Economics) because you'll specialise in the area of your Bachelor.
I hope that helps. If not, I'd recommend attending some open days and speaking to guidance counsellors if you can.
Edit: Personal note, don't take the longest route. 6.5 years to complete your degree means you'll be nearly 25. Teaching placements make it very hard to work in the later part of your degree, and (as someone who has been at uni for 5.5 years now) it is hard to see everyone else starting their careers when you are further behind. If you are passionate about everything you study go ahead, but don't study everything and anything just for the sake of it.
