I'm not him but to me the big thing that Firebase has and AWS Lambda doesn't is Firebase - a database.

Firebase Functions === AWS Lambda but it's only one of 17 components that is Firebase.

Also, Authentication component is nice (easy way to implement accounts/login with Google/Facebook/Twitter/email).

Firebase is very much easy to get started for mobile apps. You have nice console to create project, and as developer you deal with just its SDK, one CLI and simple API. For something similar to Firebase in AWS, you need to make use of Lambda, API Gateway, DynamoDB, Cognito separate products, which has steep learning curve. And then you need to know the AIM security to get started. AWS has a Mobile Hub product which is trying to make things easy to create mobile apps by automate some of these AWS products for you. So now you have to learn awsmobile CLI tool on top of the core awscli tool. And if you develop for the web, they have this AWS Amplify Javascript library on top of basic JS SDK library which has a higher abstraction thus to make things simple (or worst). If you're new to AWS, you often struggle with which library should one learn and use. And if you use AWS Ampify and read the documents, it is as if the library is build for React. I'm not sure why AWS can be so married to one web stack. So much emphasis and priority is given to React and React Native in this library. They will give the excuse that React is what their customer wants. They now have mature React/React Native Amplify library thus giving the impression that to use AWS its better to use React/React Native. So they spend resource on AWS-Amplify, even move one of JS cognate-identity-js SDK under this umbrella, hoping the world will standardised on JavaScript and React Native for iOS, Android and web. So what happen if you're developing a mobile app using Unity, Xamarin and Flutter? No luck as they only have SDK for iOS, Android and web. Compare this with Firebase that has SDK for iOS, Android, web, Xamarin, Unity, Flutter and C++. AWS has an opportunity in AppSync to make a product as easy to get started as Firebase. What is required is native mobile SDK for iOS, Android, web, Flutter, Unity, Xamarin that is not just specific to AppSync and GraphQL, but also add in authentication, analytics etc APIs. Something like Firebase SDK API. AWS is still stronger for enterprise usage. And you can’t use Firebase in China due to its use of Google Play services. But Firebase is definitely a weapon used by Google to draw customers into other Google Clouds offering.