Is it permissible to choose a traditional, interest-based (riba-based) bank that does not charge fees on current accounts, or a participatory "Islamic" bank that does charge fees on current accounts (with a free but limited-feature savings account available), when one wishes to change their current interest-based bank?

It is not permissible to deal with usurious banks; rather, one must immediately switch to Islamic banks, for the fundamental principle regarding Islamic banks is that they operate according to the provisions of Islamic Sharia. A Muslim must investigate to choose the best of these banks in terms of adherence to Sharia regulations. If a Muslim finds an Islamic bank, it is not permissible for him to deal with usurious banks, based on the ruling of the Islamic Fiqh Academy that prohibits dealing with usurious banks when an Islamic alternative is available.