I had never given much thought about the difference, but 両替 is used when referring to "actually" converting money into another currency like one may do at a money exchanger while 為替 is more a concept of exchanging foreign currency. So, for exchange rate, you use the latter; the bank quotes their exchange （為替）rate but they don't exchange （両替）money unless you ask them to. In other words, you exchange money（here you actually convert money, hence 両替）using the exchange (為替) rate .

Since the term is used for a signage that indicates the services the bank offers, 外国為替 (foreign exchange ) may be better, because this is more wide-encompassing than just 両替. (It "implies" that they do telegraphic transfer instead of just exchanging cash at the counter, and most likely they also offer foreign currency accounts.)