[nonlinear]

So... all I can get is that for the conjugate base of each, the lone pairs would reside in a sp3 and a p (?) orbital respectively... and p orbitals are higher in energy than sp3 orbitals are... I don't think this is an adequate explanation though. Can somebody explain this to me? Thank you!

[Telamond]

What about the other things present in the molecule? Does any of those orbitals overlap with the ones of nitrogen?

[nonlinear]

I'm not sure what you mean... the molecule on the right has resonance involving the nitrogen atom, but the N on the left molecule doesn't...? Could you elaborate, please?

[frisbee]

One explanation would be that in aniline (conj. base of left molecule) the nitrogen lone pair (in a p-orbital) is delocalized into the benzene ring stabilizing it compared to pyridine (conj. base of left molecule) whose nitrogen lone pair is in a sp²-hybrid orbital and is not delocalized. In other words, the pyridine nitrogen lone pair is more availble for sharing since it is not delocalized.