The first element of comparison is that they are both couples (in a non-erotic sense). They are tightly bound together and depend on one another. Their relationships are complicated, seeming to blend love and hate. They have been paired up for many years; one has a sense of such a deep familiarity that they can anticipate each others' thoughts and reactions, and they find that familiarity both a source of comfort and claustrophobia. They both are sustained by the relationships and feel trapped within them. They also almost possess private languages which the audience can overhear but not fully comprehend.
The main difference between the two relationships is that Vladimir and Estragon are equals, in similar situations, and the relationship of Pozzo and Lucky is unequal, with one being master and the other slave. Even when the positions of Pozzo and Lucky are reversed, they still remain inherently unequal.
1. The idea of 2 is absolutely crucial in Godot. There are two hats, two pairs of shoes, two acts and may be two Vladimirs, two Estragons and Two Luckys and Pozzos. At this level of the two, the two couples are one. They foil each other.
2. Didi-Gogo express a kind of eagalitarianism whereas the Lucky-Pozzo couple is a study in the master-slave relation.
3. But in a different way, the love-hate relation is operative in both. Didi and Gogo cannot help encountering each other in what looks like a scarcely populated earth. They want to drift apart but a strange love and care bind them. On the other hand, Pozzo is mortified by Lucky's passivity sometimes. There is a dependency at work here too. When Lucky speaks his thought aloud, his master just cannot take it.
4. Didi-Gogo act out a certain kind of stasis in the play in relation to which, the other couple undergoes radical changes in the second act. Lucky's dumbness and Pozzo's blindness in the second act is a pointer of change that takes place almost imperceptibly. As Pozzo despairingly says, he just went blind one day and Lucky dumb on another.
5. The Didi-Gogo pair waits, while Pozzo's famous maxim is one of movement, as his 'on' suggests in the first act. But it is this transition that disempowers his world in the second, as we see in his lecture on twilight.