When Should We Use a Repository and Factory in Magento 2?

 If there is a repository and it does what you need well, always prefer the repository.

Repositories are part of the *Service Contracts* (they are implementations of interfaces in `Api`), this means they are meant as a public interface to other modules.

# Use Repositories for full loading

`$model->load()` is not part of the service contract. I had a question on that particular topic, you might find the answers useful: https://magento.stackexchange.com/questions/111286/is-there-ever-a-reason-to-prefer-model-load-over-service-contracts

# Use Factories to create new entities

Repositories do not come with methods to create a new entity, so in that case, you will need a factory. But use the factory for the *interface*, such as `Magento\Catalog\Api\Data\ProductInterfaceFactory` - it will create the right implementation based on DI configuration.

Then use the `repository->save()` method to save it.

# Use Collection Factories if you need more control

The following is not official Magento best practice, but currently, repositories do not give you fine control over what to load. The search criteria API lets you define filters, but for example, there is no way to select particular EAV attributes or specify which index tables to join. 

These are implementation details, hidden from the service contract APIs, but often these implementation details matter and you get poor performance if you ignore them. For that reason, as soon as the repositories are limiting me I don't hesitate anymore to use the underlying collections.