I’d say, compared to Power BI, you have the ability to develop more custom and complex Dashboard / Visuals. Plus, data analytics, like trend line slope, are easily reported and comparable with something like Dash. (PowerBI will graph the line, but will not tell you the slope). You are also not confined to what they define as how you can represent the data.
Also, I dont know how many people this affects, but you cannot merge data from a database on multiple columns… the only way to do so is to create a concatenated column which merges the two to combine with another table. And… if you have automatic refresh enabled, if there is an import error, it will stop importing all tables.
With Dash, you also have the ability to download all the backend data as it gets filtered (requires callbacks of course), but PowerBI you are forced to download the data that is displayed in the chart (IMHO completely useless).
PowerBI, if you want to use formulas to manipulate the data, you have to learn a new language DAX. Obviously, this has its own hurdles… Dash, you get the prebuilt functions of whatever library you are using (typically Pandas), plus whatever other complex libraries you want to use to manipulate the data.
PowerBI vs Dash Open Source. PowerBI is $10/user/month even if all internal users, for pulling up the data. Dash Open Source, you have to pay for the hosting, but anyone on the network now has the freedom to access your analytics. Obviously, if you need to enact permissions, there is some developmental lift on this, but you are in control as the developer and not confined by the licenses.
PowerBI vs Dash Enterprise, in DE you pay per developer (if I remember correctly), not per user accessing your visualizations. In this sense, you could be sharing to 5 or 5k, it makes no difference.
Flexibility in the browser, you are in control of things like Session/Local/Memory persistence.
PowerBI does offer the ability to create visualizations with drag and drop flexibility, and can be a good starting point for understanding your data. There are a couple of Dash libraries that can also allow for some drag and drop of visualizations, but not as in-depth of a process compared to PowerBI. With DE, you do get this though.
With all this said, Dash is not just for visualizations, but can enhance your entire webapp if you wish to do so.
I cannot compare to Tableau.