All of that to say, is on the surface the two tools do a similar thing, their approach is very different. Spinnaker seems to provide an opinionated path with a slick UI and guard rails. While Pulumi is much more flexible. (For example, rather than defining your deployment pipeline in a wizard, you could write the Pulumi program to deploy resources in steps/phases.)
Anyways, there are certainly several features and capabilities that you can do in Spinnaker that we want to make easier in Pulumi. For example, supporting rollback as a first-class thing. Or pre-canned rules for switching an autoscaling group from version X to version Y.