To compare and contrast determinism and libertarianism as difficult as comparing and contrasting apples and the kitchen sink. Determinism is a description of how the world operates and libertarianism is a political philosophy advocating minimalistic government. The more typical comparisons are between determinism and free will and libertarianism and authoritarianism.
Libertarianism is a political philosophy, expounded in its most extreme (and dogmatically irrational) form by Ayn Rand, arguing that citizens should have as much freedom as possible and that the strong should be allowed to be unfettered from the necessity of helping the weak.
Determinism is the notion that our actions are completely determined by either divine (in the case of the Stoics, Calvinists, etc.) or biological and other intrinsic factors (Freud, Darwinian psychology, behaviourism) and that free will is an illusion.