Cloud Run is a managed compute platform that enables you to run containers that are invocable via requests or events. Cloud Run is serverless: it abstracts away all infrastructure management, so you can focus on what matters most — building great applications.

AWS Lambda is a serverless compute service that runs your code in response to events and automatically manages the underlying compute resources for you. You can use AWS Lambda to extend other AWS services with custom logic, or create your own back end services that operate at AWS scale, performance, and security

​You can use AWS Lambda to build mobile back-ends that retrieve and transform data from Amazon DynamoDB, handlers that compress or transform objects as they are uploaded to Amazon S3, auditing and reporting of API calls made to any Amazon Web Service, and server-less processing of streaming data using Amazon Kinesis. While execution environment reuse is useful, you should not depend on this for performance optimization. Lambda is a high availability service that manages execution across multiple Availability Zones in an AWS Region. Depending upon aggregate customer traffic, the service may load balance a function at any time.

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Google Cloud Run has it's own pricing calculator with a variety of options for those who are interested. Here.

Three different tiers, including a Free Tier, which includes:

• ​First 180,000 vCPU-seconds free per month
  
• First 360,000 GiB-seconds free per month
  
• 2 million requests free per month
  
• 1 GiB free egress within North America per month
  

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Free Plan

The AWS Lambda free usage tier includes 1M free requests per month and 400,000 GB-seconds of compute time per month.

Paid Plans

Requests: $0.20 per 1M requests
Duration: $0.0000166667 for every GB-second
Data Transfer: Lambda@Edge request pricing is $0.60 per 1 million requests. (This is run functions on all the data center edges)

Example pricing:

AWS Lambda is very cheap, and 1 million invocations with the average time of 500ms and 128 MB of available memory distributed from edges would only cost approximately $1.79 USD

Onboarding

Great tutorials and accessibility, you can quickly go into production with this.

Scalability

Automatic scalability.

Regions

Servers available currently on Asia, North America and Europe. Each Cloud Run service resides in a region. Customer data associated with this service is stored in the selected region. You can serve traffic from multiple regions by configuring external HTTP(S) Load Balancing.

Backups

Includes automatic and on-demand back-ups.

Security

Includes authentication overview,, access management, ingress restriction, encryption keys and more. Mount secrets from Secret Manager. Only deploy trusted container images with Binary Authorization. Bring your own encryption keys. Container instances run in a secure sandbox isolated from other resources, with dedicated identities and permissions.

Onboarding
AWS is famous for its detailed documentation, working code examples, videos, guides, tutorials and training plans. Onboarding will be easier and it will not take time be up and running. 

Scalability
AWS Lambda is designed to use replication and redundancy to provide high availability for both the service itself and for the Lambda functions it operates. There are no maintenance windows or scheduled downtimes for either. AWS Lambda is designed to run many instances of your functions in parallel. When you update a Lambda function, there will be a brief window of time, typically less than a minute, when requests could be served by either the old or the new version of your function.

Regions
The AWS global infrastructure is built around AWS Regions and Availability Zones. AWS Regions provide multiple physically separated and isolated Availability Zones, which are connected with low-latency, high-throughput, and highly redundant networking. With Availability Zones, you can design and operate applications and databases that automatically fail over between Availability Zones without interruption. Availability Zones are more highly available, fault tolerant, and scalable than traditional single or multiple data center infrastructures.

Security

Cloud security at AWS is the highest priority. As an AWS customer, you benefit from a data center and network architecture that is built to meet the requirements of the most security-sensitive organizations.

• Use the programming language of your choice, any language or operating system libraries, or even bring your own binaries.
• Leverage container workflows and standards
  
• Pay‐per‐use
  
• Fully managed
  
• Fast autoscaling
  
• Integrated logging and monitoring
  
• Process web traffic
  
• Process asynchronous events
  

Lambda runs your code on high-availability compute infrastructure and performs all the administration of the compute resources, including server and operating system maintenance, capacity provisioning and automatic scaling, code and security patch deployment, and code monitoring and logging. All you need to do is supply the code.

• No servers to manage.
• Continuous scaling
• Cost optimized with millisecond metering
• Consistent performance at any scale

AWS Lambda is a serverless compute service that lets you run your code without worrying about provisioning or managing any server.