So I have experience with both of the tools, since I had to demo at my company to explore the differences between them and I am certified in QlikView (so I will be more biased towards QlikView of course
) and I'll try to explain things from my perspective.
First of all.. I assume you mean QlikView Desktop because Qlik, a company behind QlikView has number of other products, and recently came out with Qlik Sense, which targets market similar to tools like Tableu, so more focused on ease of use and visualizations across variety of platforms.
That said, I will answer your question about QlikView Desktop.
QlikView Desktop comes with prebuilt scripting languague which is top class.. it's like SQL (but I find it easier to use) and has tons of functionality around data management, cleaning and eventually what you neet to do in QlikView... build data model by joining data from various data sources.
While in Power BI you create your own apps with extending Excel and creating behind-the-scene model, in QlikView you use the scripting language and all your data (including Excel) resides outside of the QlikView application. You use reload button to extract that data from outside into QlikView application (but there are also variations here, you can store that data externally into special QVD files etc...)
I find that much better since I can easily sort out different Excels in folders, give people in organization access to these folders, and change scripts in QlikView that load the data and model at one place
So the way you build the model is different, you have more power and better control through scripting.
Second difference is, the tools like slicer you have in Excel, this is just a slight of hint what you can do with QLikView's associative analysis. QlikView is built all around that kind of logic, you click something, everything changes according to selection... then on a top of that you have many more ways to visualize data, an there is this thing called set analysis which is such a powerful tool in QlikView (books written about it) that you can do amazing things in representing the data. Also, QlikView is very very fast with large data sets.
I almost exclusively use QlikView for Data analysis in company projects, even to check how customer's data is modeled or if it needs cleaning etc.
I would use PowerBI in case to do simpler my-own analysis or, Microsoft Power BI is built into some other enterprise softwares like ERPs where models come out of the place (product cross-sales from MS)
I have course on the topic on Udemy and there is a free chapter you can see about associative model difference between Excel and Qlikview here, so if you are interested check it out (I have put discounted coupon to it)
https://www.udemy.com/qlikview/?couponCode=THE29DEAL