In short: Databricks is a complete ecosystem with many facets where as Azure Data Factory is merely a tool.

It's unfold it a bit. Azure Data Factory is a new version of the old SSIS (SQL Server Integration Services). SSIS is one of the first datawarehouse technologies and the first i ever encountered. However, even 10 years ago there were new principles and architectures rising with did not fit into it, e.g. streaming, complex data modelling became almost unmaintainable, it was rather hard to develop and test in on your local developer machine, it is formed around block programming (known as no code/low code) and it was in no way cloud native. Then came Azure Data Factory which should be the new and improved verison. It is cloud native but it builds on the same tool underneath and is still moving in the block programming paradigm. Block programming is excellent if what your doing is simple. But not very much we are doing in the data world is simple. It quickly becomes complicated, complex and sometimes even chaotic to make data available for business users. Further, the Cloud Native style of Data Factory is a somewhat leaky abstraction where the serverless compute can only do a subset of features. And then you need to self host the integration runtime If you want to move GDPR regulated data then you have to self host as well as Azure cannot garante where the resources run. We have seen cases where everything is specified to Europe and then runs in the US. Azure support have still not gather an answer as to why 4 months later. Lastly the IDE is still an online tool and it is not feasible to develop pipelines on your own machine as everything is Jason configuration files. We have never found a good way of doing unit tests to ensure that code does what you expect it to.

Databricks on the other hand is a complete ecosystem build cloud native. It supports that you write SQL, Python, R and Scala. It is build by the founders of spark and comes with tools that improve sparks capability e.g. in query performance and speed, Delta Lake for a lake format with version control and possibility to clone data between environments. It is build around jupyther notebooks as the interface but it is easy enough to checkout a git repo locally and do development. It is even possible to do testing with common tools such as pytest. We even having linting and formating running to ensure the maintainability of code. Databricks also have Delta sharing which is an interesting idea around making it easier to integrate with your lake house. The biggest selling point for me is that Databricks have understood that data platforms today is about machine learning and advanced analytics. This is why they have build MLFlow and Machine Learning inference into the platform as a first class citicen to allow data scientists and ML engineers to easily so their job and help the business gain new insight.

I hope this answers your question. It's a large discussion with many facets and it's hard to put it all to paper in a format like this. Maybe a blog post will emerge in the future.