We're with AAMI for everything. They're not the cheapest, but we have never had any problem at all claiming. They're quick and the repairs are always good.

FWIW - My aunty was insured with RACV - they only found out their car was a write-off when they came across it being driven to a wrecker on the back of a tow truck. The repair was only one side front panel worth of damage. When my aunty brought it to the attention of RACV, they got it back from the wrecker and fixed it. Lucky they saw it being towed there! Another friend was with RACV too and they accused him of stealing his own car when he reported it stolen. I like that I can ring my insurance company and they smile over the phone.