First things first, they are both aromatic so that can't be the reason why pyridine is more stable than benzene. However the lone pairs on the Nitrogen do not contribute to the cyclic system since they are orthogonal therefore when it is protonated (having a plus charge on the nitrogen), its lone pair of electrons with another hydrogen would not disrupt the system making it still stable whereas a benzene ring when one of its bonds is broken the plus charge on it ruins the aromaticity which makes it less stable.
I hope this is clear enough to understand. This is the way that I understood why pyridine is more stable than a benzene ring. If you have trouble understanding this just send me a private message then.