Out of the box mapping is miles better in Tableau.

Overall Tableau is more fully-featured than Power BI. Tableau aims to be a complete BI presentation layer. Power BI is positioned as the self-service and personalized consumption component as a part of a larger BI presentation layer. Microsoft would prefer that the entirety of the BI stack be made up of their technologies, but Power BI can consume other data sources, and its reports can be embedded in other apps, so it fits into other technologies as well.

We could go feature-by-feature and Tableau would win the majority of presentation sophistication bullets (more fine-grained control of display, filtering, interactions - richer collection of built-in visualizations).

The differentiator for Power BI is more on the self-service end. Personalized dashboards (dashboard and report are two distinct concepts in Power BI) can be trivially created from published reports. Customized reports can easily be extended from published reports and datasets. There's a strong collaboration framework based on Office 365 groups and with lessons learned from SharePoint. There is also a pretty seamless upgrade path. Power Pivot models can currently be promoted to SSAS, and the expectation is for the same to be possible with Power BI models (all the same backing database technology).

I hate to be so vague, but there's a lot to both products. I'd be happy to dive deeper into some specific cases if you've got questions.

It all boils down to this, in my opinion: PowerBI is for dashboards and reporting mostly. Tableau can do dashboards, but it can also do "analysis". Uncovering insights in the data that go way beyond simple cross-filtering.

In my mind, they are different tools for different purposes.

I'm not saying that to bash on PowerBI. I love that product and use it heavily and promote it to clients. It just serves different purposes than Tableau.