A similarity between the two thinkers is that they, each in his own way, in their best works assume that ‘meaningful order’ in this world is not taken for granted.
For Levinas – in Totality and Infinity – this notion is alive in his description of an elusive but constant alternation of two principles: that of self-centeredness and the breaking thereof by the Other. The Other keeps constantly surprising you, precisely because once and again after each break you, fully legitimately, return to your ego-zone. Structures of the ego – and by extension of the state and institutions – are important, but the other can – in His completely unpredictable way – disturb them and claim the (temporary) primate.
This realization that our own finite life in the light of indifferent eternity means nothing, was in the very same Parisian environment already articulated by Sartre. He believed that we can only tolerate that awareness as ‘disgust’ (la nausée). Camus elaborates the theme in several books, and his main conclusion is that it is important for people to bear this absurdity, in a as human as possible way.
Indeed, Camus himself did the bearing. Till the end he has refused to take easy positions, such as regarding the Algerian war for independence or towards communism. For that, he was too much aware of the precariousness of many viewpoints. Very different, for example, from Sartre who at some point shied away from the lonely-making aspects of his own existentialist thinking and preferred the full, but often oversimplified commitment of communism.
Unlike Camus, and more like Sartre – but in his own unique way – Levinas ultimately succumbed to the temptation of a less absurd and elusive universe. In his book Otherwise than Being he takes leave from the fragile anarchistic balance of Totality and Infinity, and he chooses to attribute a unequivocal depth structure to the life of every human being. We are “deeply” and “before everything” dedicated to and to the disposal of the Other, Levinas says in that book.
I regret this development in Levinas. Firstly, because I cannot sympathize with the total commitment to the other, indeed: to every other. That doesn’t tally with my experiences. Secondly, because the anarchist balancing of Totality and Infinity seems to me more realistic, mostly because of the message that we must endure that uncertainty. Pity that Levinas in his later work succumbed to the lure of more grounded theory.
That has not happened to Camus. Perhaps because died at much younger age?
Also see Professional Philosophy's sad Course: Nussbaum and Levinas