It's not an obvious exercise. How "important" is migration and home affairs compared to the internal market? The internal market is certainly at the core of the competences of the EU, but maybe it's in the less established areas that more interesting developments are happening. Furthermore, they might suddenly become extremely relevant. Nobody predicted how important DG SANTE would become in 2020, for example.

One indicator of importance might be staff size. I struggle to find a good and up to date figure right now, so I'll make do with a pretty bad and outdated one from 2020, showing the size of the staff under each Commissioner at that point in time. Johannes Hahn runs the largest operation as the DG of budget and administration. Budget is unquestionably important. Administration as well, but it might produce more staff than power.

The Commissioner for Innovation, Research, Culture, Education and Youth comes in second place. The Commissioner for International Partnerships comes third.

So these positions run the largest operations. Linking that to power is probably somewhat misguided - it would indicate that all three of these relatively anonymous positions were more important than von der Leyen. Entering a position with a lot of staff might even decrease your power, as you are forced into a role that might have more to do with management and less to do with politics; furthermore, if the field is already well-developed in the EU, it might not be where central developments are happening going forwards.

A better indicator could be to go through the Directorate-Generals under the control of the different Commissioners. The Commissioner of the Internal Market, for example, is also responsible for for the Directorate-General for Defence Industry and Space. That might be important these days.

In the traditional competences of the EU, the DG for for Maritime Affairs and Fisheries would be considered very important. These days, and especially on this platform, people might be more interested in the DG for Communications Networks, Content and Technology.

Wherever Union competences are weak and/or anonymous, there's greater room to innovate and to surprise us by striking some crazy deal. In politicized issues that we intuitively care about, the Commissioner's power will also be relatively weaker as they are kept under strict control. So there's an inherent tension: The fact that a Commissioner is widely considered as being important might actually make them less relevant by making it harder for them to pursue an agenda. They might end up just striking smallest common denominator compromises with all involved actors, and have little to say themselves for the outcomes as such.

So that's a messy non-answer, and I guess nobody is any wiser. But it's difficult, in my opinion, to give a very clearly defined answer which positions are important and which are not.

I think an important one to look out for is who are the vice presidents. Those (and their posts) are probably the more important ones.

Other important people are the Parliament president and the president of the Council (roughly equivalent to a country's senate). Understanding the three bodies of Commission, Parliament, and Council is the lowest hanging fruit towards understanding the EU in general.