Classical pianists are faced with the rigorous task of sight reading. Sight reading includes being completely fluent in reading rhythm as well as melody. Reading sheet music is probably one of the most arduous and tedious tasks of playing classical music. Because classical music relies almost entirely on sight reading music written by previous master composers such as Mozart, Hadyn, Bartok, Bach and the like, there are many guidelines as to how songs should be played. Advanced classical technique is also very strenuous and complex. Some advanced pieces may take an average classical pianist several months to learn.
Jazz relies heavily on improvisation. Because jazz is more free spirited and in the moment, many think that it’s easy. Coming from a classical background, this is definitely not the case. Complex chords are often used in jazz music that are never found in classical music. Extended chords such as 9ths, flat 13ths etc. would sound quite dissonant to a classical ear. If Beethoven or Mozart had heard jazz piano played, they might have wrinkled their nose a bit pondering questions of harmony before really taking a liking to it. It definitely took some acclimation for me to appreciate this style of music.
One of the most complex things about jazz is theory. Although students of classical music learn a lot of theory, not much of it is actually used because students are not reliant on theory to play their pieces. All they have to do is learn music from sheets and then commit it to memory.
As for jazz, there are so many different chords and inversions that students will need to learn before being able to improvise melodies and rhythms over them. Understanding music theory is a very integral part of playing this form of music. Jazz chord changes are also very complex and irregular compared to traditional classical piano pieces. Though both advanced classical and jazz students will know all the scales in different keys, jazz musicians will use this knowledge in a more hands on way than an average classical pianist.
Finger technique for both genres can be extremely difficult. In my opinion, neither of them is harder than the other although many classical riffs may be a bit more complex as jazz melodies are often created by running scales. Learning complex classical and jazz riffs will take much dedication and practice to master and proper finger technique will dictate how well one can play for both genres.
In conclusion, the two genres have different obstacles and challenges that students will have to surmount and face. I would say both can be equally as challenging but just in different aspects. A real master pianist will have comprehensive knowledge of both.