They are both very known for their color photography. They both as photographers capture images of unexpected daily moments, involving people or significant locations. That being said, they both have this relation and similarity of both making the reader of the picture wonder: "what is going on?"
Here's one of Meyerowitz photos:
Heres one of Egglestons photos:
Can't you see the resemblance? Two different objects, set up in two different locations, but leave the same effect on the person observing the picture.