So I was wondering, I am running a moddafied Han shoots first run. But was wondering why having Chewbacca on my crew is better then just shelling out the same 4 points for a shields upgrade?

Because he costs the same but is more than twice as good as a shield upgrade. With shield upgrade you only get 1 shield. With chewbacca, you get to avoid a hit (probably a crit) and at the same time get a shield back. You get an extra shield with both, but you also get to avoid an important hit with chewie.