They’re actually pretty different. Elastic Beanstalk is intended to make developers’ lives easier. CloudFormation is intended to make systems engineers’ lives easier.
Elastic Beanstalk is a PaaS-like layer on top of AWS’s IaaS services which abstracts away the underlying EC2 instances, Elastic Load Balancers, auto-scaling groups, etc. This makes it a lot easier for developers, who don’t want to be dealing with all the systems stuff, to get their application quickly deployed on AWS. It’s very similar to other PaaS products such as Heroku, EngineYard, Google App Engine, etc. With Elastic Beanstalk, you don’t need to understand how any of the underlying magic works.
CloudFormation, on the other hand, doesn’t automatically do anything. It’s simply a way to define all the resources needed for deployment in a huge JSON/YAML file. So a CloudFormation template might actually create two Elastic Beanstalk environments (production and staging), a couple of ElasticCache clusters, a DynamoDB table, and then the proper DNS in Route53. I then upload this template to AWS, walk away, and 45 minutes later everything is ready and waiting. Since it’s just a plain-text JSON/YAML file, I can stick it in my source control which provides a great way to version my application deployments. It also ensures that I have a repeatable, “known good” configuration that I can quickly deploy in a different region.