I guess the WALL-E units were like that because they were built to be more sturdier and tougher to survive the harsh environment on Earth with all the weather and stuff while the Axiom robots lived in a complete artificial environment. As for WALL-A (big one), they had the eyes as spotlights to see in the deep garbage chambers of the Axiom.

Why do the waste allocation load lifters(Earth class) Have no screen eyes while the axiom class has screen eyes