It's incredibly difficult to find places to live in Chch at the moment, unfortunately. Most of the people I know agree that there is a property shortage in Chch like never before. It'll be worse if you are trying to find a place from overseas. The winter weather is okay, mild by Canadian standards, horrible by Australian ones.
Auckland has much milder winters and less fluctuation in temperatures.
There are pros and cons to each; some of the Chch suburbs are incredibly beautiful in the way it seems only the South Island can be (at least to me), and it's a much more relaxed place, but Auckland has the city life and all the benefits that come with that.