What is the difference between Pangloss and Martin as philosophers in Candide?

Pangloss and Martin have two conflicting viewpoints on life and on the nature of the world. Pangloss is the champion of optimism (and a mocking satire of Leibnitz). For Pangloss, this world must be rationally understood as "the best of all possible worlds"—a position through which he would rationalize away the suffering and misery that surrounds him. At times, this philosophy even forms a kind of willful delusion.
In addition, there is a kind of irrational absurdity that underlies Pangloss's demonstrations. We see this on display in the first chapter, where he gives a lengthy argument to demonstrate that, just as this is the best of all possible worlds, so too is the Baron's castle the best of all possible castles, but this entire line of argumentation amounts to nonsense. Pangloss is a fool, and at times a dangerous one, given what he argues and the way in which he would justify the suffering and cruelty of the world.
Martin's viewpoint is very much the opposite of the Pangloss's: if Pangloss holds that this is the best of all possible worlds, Martin would hold that this is the worst. For Martin, misery is the defining inescapable truth of the world around him, and happiness is ultimately ephemeral. To a certain degree, one might hold that Martin, in addition to being more pessimistic, is also more of a realist than Pangloss is. Pangloss's philosophy is informed by rationalism and abstract speculation. Martin's perspective, on the other hand, has been shaped by his own experience of suffering and the suffering he sees all around him.
That being said, in its own way, Voltaire's narrative condemns Martin's reasoning just as it does Pangloss's. Early on, Martin defines himself as a Manichean (chapter 20), but it's worth noting that, on technical terms, Martin has mislabeled himself. Manichean cosmology implies dualism and the struggle for mastery between good and evil, but for Martin, this bifurcation does not exist—there is no good, only evil. This is not an unimportant detail, but rather a subtle hint that Martin himself might be deluded in his own way, just as Pangloss is in his. Martin's mistake, I would hold, is that his pessimism is ultimately self-defeating, because even if he recognizes the injustice and cruelty of the world around him, in his pessimism, he is unable to seek out an alternative, or to oppose it, or to do anything constructive in the face of it.