voigstr, how accessible are these 2 banks?
I don't see a lot of merit in banks that would be hard to access. Or that will charge you to access funds in Offset through ATM's - I've never seen AMP or B&E ATM's  Although I do identify that B&E is tassie based.
I would recommend Suncorp, as I am a fan and a customer and a shareholder and a former staff member. But they really only specialise in QLD and I feel they don't yet have the exposure nationwide. So prob no good in Tassie.
Go with somewhere you feel is accessible, fees are fair and they are big enough to provide security.
I've had friends who ended up with ING, BankWest and Adelaide Bank (while living here in NQ). When something went wrong, they couldn't go to a branch, they had to wait 2-3 days for transfers and ended up being sick to death of calling call-centres...
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