There are different cases for using both depending on the specific needs and requirements, Synapse and Databricks are similar, but both have their own areas of specialities or rather areas where they are above the other.
Data Lake – they both allow you to query the data from the data lake, Synapse uses either the SQL on demand pool or Spark and Databricks uses the Databricks workspace once you have mounted the data lake. If you are predominately a SQL user and prefer the code and the BI developer feel then Synapse would be the correct choice whereas if you are a Data Scientist and prefer to code in Python or R then Databricks would feel more at home.
Read on for a nuanced take. My less nuanced take is, Databricks beats the pants off of Synapse Spark pools in terms of performance. Synapse has a much better overall ecosystem, expanding beyond Spark and into T-SQL (in two flavors) and log/event analytics with KQL. If you’re spending 100% of your time in Spark and don’t care about the rest, use Databricks; if Spark is a relatively small part of your warehousing work, use Synapse.