I have been working on learning the Deal.ii library. Why? Because it is one of the most advanced finite element libraries I have come across. It can handle adaptive mesh refinement, multiphysics, hex-dominant, and open source. This level of detail in an open source library is amazing. If you want to buy commercial software equivalent, then you are looking at $50-100k.
The barrier to Deal.ii is that you need to program in C++. Ouch. So that learning curve is steep. I have to learn the build system, a C++ IDE, C++, and Deal.ii all at the same time. I think it will be worth it.