This is a great question -- thanks for asking.

GCF provides a different experience where you provide just snippets of code and you don't have to even build a full app. Of course, this has pros and cons. The pros are that it's easier to get started, and the service manages things like language runtimes for you. But, the number of languages is usually limited, and you can't customize the OS packages you're including.

In Cloud Run, you provide an entire container. But, this means you're responsible for the contents of the container, which means you have to roll out updates if there there is a security issue for a language.

The two products actually run on the same underlying infrastructure. And, with the open source JavaScript functions framework, you can have a GCF-like experience on Cloud Run. https://cloud.google.com/functions/docs/functions-framework

This was actually the subject of a talk I did last month at ServerlessConf (containers vs. functions), but unfortunately the video hasn't been posted yet. (It'll be posted at https://acloud.guru/series/serverlessconf-nyc-2019.)

From what I understand they serve different needs. One is deployment at the container level and the other is at the functions level. Both use HTTP as the communication layer. Depending on your workload there are good reasons to choose either.