Python 3, 62 47 57 bytes
Edit: - 5 bytes thanks to @Mr.Xcoder
Edit: +10 bytes to fix a bug
lambda x,y:({*"abc"}-{x[:1],y[:1]}).pop()+(x[1:]or y[1:])
Edit: - 5 bytes thanks to @Mr.Xcoder
Edit: +10 bytes to fix a bug
lambda x,y:({*"abc"}-{x[:1],y[:1]}).pop()+(x[1:]or y[1:])