Different expression languages are available, such as Data Analysis Expressions in Power BI and Qlik sense expression syntax (QLik script & Set Analysis). Each has its forte and differences based on syntax, ability, and performance.
Moving from the point of syntax and structure, DAX in Power BI is a little more structured and bears a functional resemblance to Excel formulas. It does row-wise calculations and aggregations over relationships. Qlik Sense affords its expression more flexibility with dynamic aggregation in filtering through its unique design of combining Set Analysis for filtering and Load Script for pre-aggregating data, albeit requiring an entirely different state of mind compared to DAX, which works out of table-wise operations.
How the models handle data: Power BI relational models have tables with relationships, and the DAX calculations depend on contexts most of the time. Qlik Sense is an associative model where all fields associate with one another dynamically so that the user can interact with the data without having to define relationships in explicit terms, which inherently makes cross-table aggregations more intuitive.
By performance and flexibility aspect, DAX has a very high calculation performance but may get tricky with many-to-many relationships and context transition issues. Qlik Sense, however, performs faster in-memory data processing; hence, it becomes useful for larger-scale exploratory analysis, although advanced Set Analysis can have steep learning curves for the new ones.
To summarize, Power BI's DAX suits more structured reporting needs, while Qlik Sense expressions and its associative model provide much more flexibility in ad hoc analysis.
