I am using Azure Table storage to store the data of my application. I need to build an API to retrieve the data from Azure table storage. There are like a million records in the table. In the initial stage, my API would be getting approximately 100-1000 hits per day. What would be the best choice to develop that API on, API apps or Service Fabric?
It depends on a lot of aspects:
As described by @feranto the main difference is the architectural pattern. The decision will have a lot of implications for you, not only when it comes to development, but you will have to consider how to maintain your application.
Only based on your short description, it sounds like a relatively straightforward solution and not very complex nor very high performance/scale requirements. Given that, it might be easier for you to go for a more basic API App. Service Fabric is an excellent framework and architecture that allows us to build very flexible, highly scalable solutions, but it should be noted that that also comes with a lot more complexity when it comes to handling, monitoring and maintaining both the underlying service cluster and it's applications.
Setting up an API App, connecting to an Azure Storage table and control that with for instance Application Insights is relatively straight forward and you can find a lot of documentation and samples for that. As a contrast, Service Fabric is fairly nascent in documentation and samples, and you would have to read up on a lot to get a basic stable solution running if you are new to it.