Passport from a first world country, or a large bank account, which matters more when travelling?

Good passport, definitely. Firstly, very rich people from less developed countries are probably able to obtain visas quite easily because they are businessmen etc. But secondly, even with a good passport (I am English), you still need to prove that you have a certain amount of money in your account to obtain a visa, or at least that's the case for some places.