Tried that advice a few months ago, but the local credit union here (and there's only one in this entire province sadly), offered no better interest to my savings account, and wanted to charge me 3-5% more interest for any existing loans and credit cards that I wanted to more over. Guess they weren't hurting for customers too badly.
As for what bank, it's one of the five in Canada. Doesnt' matter much as to the name, they're all the same here really for anyone that isn't a millionaire.