Having learned both sax AND piano before starting guitar, I must say, guitar is the easiest to improvise with, but, for me, the most difficult to play written music with. When soloing, on guitar you can feel and watch the physical patterns of the intervals, on piano, you have the black keys (speed bumps) that make changing key difficult, and on the sax, if you don't know the notes of a key, you can NOT solo in it. Simple as that.