I think I might be showing my age here, but I quite like the Kiwibank Internet Banking interface. It's quite a simple interface as it has not changed much in a long time. In fact I am certain a lot of the Internet Banking interface is original from launch. However its fast to load (clearly designed for 2000's era connections) and you can do nearly everything you need to do with minimal fuss. It is so old fashioned it works perfectly in pretty much any browser. One feature I quite like is the level of detail you get from transactions (which other banks seem to hide) -- for example for many transactions they will show the contra (i.e. other party) account. Don't think that because the UI is old fashioned that there are no modern stuff--they have successfully retrofitted many new features e.g. TXT confirmation of large transactions, new payees, and the like.
The Mobile app is much more modern and quite slick actually.
My secondary bank is ASB for a number of reasons. I agree the ASB Internet Banking redesign is...interesting. Seems to go down the path of simplifying things to the point you can only do certain things certain ways. I'm not sure I'd be happy with it as my bank bank. Funnily enough I also have authority over a few Society accounts which uses ASB Business Banking and its entirely the opposite--the UI is so complex it took me a good 10 minutes to figure how how to make a single payment the first time I did it. And even now it takes me a few minutes to figure it out what to do when I need to make another one. Really no consistency at all and always missing the mark by a long way (i.e. too simple or too complex).
I only hope when Kiwibank eventually does a refresh they use ASB as a guide of what not to do...
I was a BNZ customer for a while a few years back and I was fairly impressed with the eye candy on their platform. However to be quite honest I can do everything online with Kiwibank that I could do online with BNZ so it's more of a eye candy thing really. I wouldn't switch just because of eye candy -- for me minimising my financial expenses is more important so I'd go with a bank with cheaper rates as long as their internet baking is decent enough.
Westpac is also a honourable mention as well, their internet banking is fairly modern by NZ Banks standards -- they were going through the process of switching over to their current platform just as I joined them so I got to see both the old platform and the new one. They seemed pretty good at keeping the old platform around until they had migrated every feature across. I ended up leaving Westpac to go back to Kiwibank only because I met my now husband and back then it made more sense to stick with the one bank we both had accounts with i.e. Kiwibank.
Been a while since I've used ANZ and Co-Operative. I recall both had modern platforms but beyond that can't recall much.
(Yes I've used too many different banks. I'm now under strict orders to stick with one!)