Azure has the best "serverless" functions platform out of the major cloud providers right now. Easier deployment process and triggers to activate a function outnumber the other vendors. The new Event Grid service allows connecting them to pretty much anything, especially when used with the Logic Apps service.

AWS Lambda is decent and has features like Lambda@Edge which runs on CDN nodes and can do processing on each request.

Google Cloud Functions are basic and only support javascript with http, pub/sub and storage triggers without any integrations beyond that or into the rest of the platform.