what are the Pros and Cons of ESPRIT and MUSIC algorythms?
The prime thing such algorithms aim to do is to make use of more information that you may have about the signal. In this case, the extra information is that you know the number of signals (sinusoids) present in your measurements.

One pro for both is, therefore, when your measurements match the assumption, you get a more accurate representation of the spectrum: it has the right number of lines. The FFT does not guarantee this.

A con is that, if your assumption is wrong (there are three lines instead of two), then these algorithms perform worse.

These algorithms do not give better resolution than the FFT. Only more data can give more resolution.

There is a good exposition here comparing the two to each other.