Which address should I use?

There's no definitive rule about trusting one data source over another. You have to use your best judgement.

One easy way out of this conundrum -- call the bank and ask! It's still not guaranteed to be correct but it might tip the scales toward one address or the other.

Regarding Andy's objection to copying address info from websites, my personal interpretation is to consider the info on a business's official website to be the digital equivalent of on-the-ground signage. Info from an in-person survey is better of course, if possible. (And as Andy mentioned, if the website shows address info using a non-OSM embedded map, or has a "click here for address" link that takes you to another map, that's definitely off-limits.)

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edit -- Just to be clear, I would strongly recommend against adding any data to OSM based based solely on websites, even official ones. Websites are easy to create but keeping them up to date is often a very low priority, so business information -- including the address, phone number, opening hours, or even whether the business still exists at all -- can be wrong.

If I've surveyed a business in person and certain info (like phone number or opening hours) is not signed, then I generally don't see a problem with taking it from the official website. Not all mappers would agree with this approach though; some will only add data surveyed in person and will urge you to do the same.

Don't use them for mapping openstreetmap because of copyright. Just use the information for a survey. You could maybe use the banks data for address information. see the wiki and https://help.openstreetmap.org/search/?csrfmiddlewaretoken=0PMIveRQEfVPyHbmbXYFVEN9qjs54ByO&q=copyright&Submit=search&t=question