Shift is a prequel to Wool and also offers a different side of the story of what happened in Wool. It partially explains how the silo came to be and where it is heading.

Shift only contains 3 parts, whereas Wool had 5, but it has about the same number of pages. This means that the stories in Shift are a bit slower. They take a little more time to get going and there's more background given.

In general, I liked Wool better, but still very much enjoyed this look behind the scenes of what happened previously. Although it's possible to read Shift first, it'll ruin your enjoyment of Wool.