I like running with Cait when I feel like being a little 'bad'. Her perk is also more useful to me than Hancock's since I never let my rads get high enough to trigger his for a long enough time to make it helpful at all.
Both are not even close to having the best companion perks in the game though. I don't like perks that only work under very specific circumstances. Preston, Danse and MacCready all have much better perks in that regard.
