Comparing basic strengths between pyridine and 1,2-dihydropyrazine
What I would do is I would compare their acid strengths. Due to inductive forces, deprotonating the 1,2-dihydropyrazine would result in a more stable compound than that in pyridine--the nearby nitrogen (electronegative) will share the burden of the negative charge. Therefore, 1,2-dihydropyrazine is more acidic and thus is less basic.