What existing businesses or products does Bitcoin compete with? I'm trying to understand who sees Bitcoin as competition to their main product.  For example, I've heard that Bitcoin competes with:


Swiss numbered bank accounts 
Deflationary PMs (precious metals)
Money transfers like Western Union, Paypal, SWIFT


What other businesses or "thing" does Bitcoin compete with?
Cash. It competes with cash.

All of these things (prepaid accounts, debit cards, bank accounts, money transmitters, etc.) are sophistications built on top of cash in order to facilitate the transfer of cash from one entity to another. It's not easy to carry cash, nor is it safe to keep all of your cash in one place. It's not feasible to give cash to someone thousands of miles away. The aforementioned services make cash more, well, bearable.

Bitcoin rolls all of these services into one. The only one still possibly useful is a bank, which is merely a trusted, secure storage for a few bytes of data: a private key. 

Credit cards and loans are a different concept. Those who have give to those who do not with the assumption that what was given will be returned, and then some. Bitcoin actually may make it more difficult for these kind of firms to operate because of its finite nature. That is, it cannot be created on the record books like fiat currency can. Fractional reserve banking within the Bitcoin model is possible, but there's disagreement on how it may be implemented.