My e-deal experiences:
I tend not to use the self checkin terminals, but have been offered earlier flights probably about 25% of the times I have. For whatever reason this has nearly always happened in Sydney.
I usually get on an 'earlier' flight in the event of delays just by asking at the Qantas Club desk, and have sometimes at other times - nearly always lightly-loaded kind of flights. I have never been shifted to an earlier flight at peak times (Mon AM/Fri PM) when things are running normally.
I've also sometimes got better routings (ie direct) even after having initially booked non-direct (for SC, or timing/convenience) but then needed/preferred the direct flight on the travel date. Sometimes it's just been offered, other times I've asked.
My experience has basically told me, treat it as a gift if you get it, but NEVER expect it - buy flexi if that's what you need : )