How many psychoacoustical critical bands are there?
Neither. The basilar membrane in your ear performs a frequency-to-place transformation which is then picked up by an array of thousands of hair cells (cilia). Therefore there are thousands of heavily overlapped bands. The processing that follows is very complex and not completely understood. The shape of the effective band pass filter at each location on the membrane can be measured in animals, and the masking curves can be measured by listening tests. Masking is measured by increasing the amplitude of a test tone relative to the masking tone until it is audible, so the situation is a bit different that what you assumed in your question (where you assumed that if the masker and the test tone were in the same band, you only hear one tone). The actual result is that as the test tone approaches the masker frequency, it must have a higher amplitude before it can be detected. 

Bob