Medical doctors in the UK and other commonwealth countries have traditionally been MBBS.
In Australia, the adoption of the Australian Qualifications Framework and pressure from the US, where people seem to expect 'MD's has lead to most universities shifting to MD programs from MBBS (an AQF level 7 -> AQF level 9).
The bottom line on this is substantively nothing, except a bit less ink being used on business cards, millions of dollars spent on website rebranding by medical schools and endless posturing by faculty for students.
So basically, whether you are a 'Doctor' by post-nominals or a 'Doctor' by recognition of your MBBS, your education has been effectively the same, and the distinction is actually meaningless.