Pre-Triggers and Post-Triggers do not take any input parameters. Since Cosmos DB needs to work more work to execute triggers, you will end up with higher Request Units for your queries. They might name triggers, but both do not get executed automatically with every operation. You need to call them programmatically if you want to run them. If trigger throws any error for any reason, transaction will roll back and data will not be saved to the database.
Naturally, triggers are going to have a performance impact on your system regardless of the choice of data platform.