Sorry if this sounds cliche but you can't really compare a sonata to a concerto. First off the sheer length of them, the need for some improvisation and thought, as well as (if you intend to) performing it with an orchestra make these completely different beasts.But in my opinion:I'd say his 1st, 2nd and 3rd concertos are somewhere around the ballpark of the Op 31 sonatas for musical difficulty, and for the technical grips I'd say comparable to the last movement of the Op. 27 No. 2 (moonlight).The 4th and 5th certainly pose more challenges (the 5th especially since it is so well known, but this may be in the performer's favour as it is such a great work even a mediocre rendition would sound amazing). For these two I'd say they are similar to the technique required for the Waldstein and Appasionata (thus below Op111, Op 106), and musical difficulty similar to that of Op81a (actually any Op 53+ sonata is musically difficult , it's just me thinking that Op 81a stands out because there's an actual story behind it written in the music)
Personally , I have played the the op. 13 23 24(sonata for violin and piano) and 58(concerto 4) entirely . Now I am about to play my first Beethoven's late sonata,op.111. My teacher tells me that technically , op.111 is the same level of 4th concerto , but still , I will encounter difficulty for sure because it is Late sonatas...Before I enter the conservatory , I also played some movements of some his sonatas, like moonlight ,appassionata ,op.2 no.1... I think that I am totally prepared to start the next phase. But why is my teacher so sure about it will still be difficult for me, I do not quite believe it. In a other word, what should I pay attention to when I work at it?
I don't know if I understood correctly, are you asking about why your teacher finds the op. 111 difficult for you?If that's the question, well... the answer is quite obvious, in my opinion But I'm someone who doesn't separate technicality from musicality, so my opinion may be different from yours.And I don't mean you shouldn't play it! I'm just saying the op. 111 is difficult for everyone.