It's quite misleading to just say "Not Necessarily". The truth is that you have to perform at a much higher percentile in Standard English than Advanced to achieve the same scaled mark. The scaled marks of each subject is added together to form an aggregate out of 500, which determines your ATAR.
For example, in 2008, to have achieved a Band 6 in Standard English you would have had to be in the 99.3th percentile, ie the top 0.7% of the state. Even then, your scaled mark would have been 84.6/100.
Comparatively, in 2008 to have achieved a Band 6 in Advanced English you would have had to be in the 89th percentile, ie top 11%, and that scales to 84.2/100 aggregate.
In other words, it is quite a lot easier to achieve a higher scaled mark from Advanced than Standard in the sense that you don't have to be ranked so highly within the state for it. Whilst one can reason that the cohort for Standard may not be as good at English as the Advanced crew, that reasoning doesn't account for this wide margin. It is definitely much easier to be in the top 11% for Advanced than to be in the top 0.7% for Standard. In fact there are many reports of even worse odds, many threads here talk about how there's only a handful of band 6's in Standard every year.
My advice would be to do Advanced if you are able to do it, not being allowed to enroll but if you think you have the capability and motivation to do some work, but if you are really really bad at English, you may have to stick to Standard. But if you can cope with the work, Advanced English will end up giving the better ATAR, most likely.