I use internode and I am extremely happy with their service. They are not the cheapest ISP on the market but they have several positive qualities which I find very useful at times. My exposure to them was due to their focus on internet gaming, which requires quality over quantity, which sums up internode very well in my mind.
The majority of their plans do not count uploads, which is nice. They generally don't do the peak/off peak thing either, so while you tend to get less total GB per month from them than you would from their competitors it is usable whenever, which generally means you get more peak downloads. As I've mentioned, my experience with them has suggested that they provide a high quality service with very little downtime. One feature that seems unique to their service that I really like is what they call 'data blocks' - extra downloads that you can purchase for each individual month on an ad hoc basis (eg: if I find myself in a situation where I am going to be capped with a week to go and absolutely need top speed internet for that week because of uni assignments or the like, I can purchase an extra 2, 5, 10 or more GB for that month). Every experience I have had with their technical support staff has been absolutely top rate too, they're always knowledgeable, polite and understandable and they often go the extra mile - one time when my mobile died mid tech support call, they rang me back 3 times, trying to get back in touch with me. Oh, and one thing you may appreciate (coming from Bigpond) is that they tend not to lock you into contracts.
I haven't looked into what iinet provides recently because I've been so happy with internode. However, when I was looking a couple of years ago, they seemed to use the peak/off peak model which means that you get more total downloads per month, if that is what you are looking for. From what I have heard from several friends, they provide a generally good service - although not of the quality I have experienced with internode; although they do have a similar quality connection.
So yeah, I recommend internode; they're very good. IInet will give you more downloads but less flexibility - but if you're really looking for *lots* of downloads, from what I have heard you can't go past TPG (who's quality of connection is not quite as good but you do get ALOT of data each month).