I believe that addition is the easiest operation to perform on functions. You need only recognize like terms and add the coefficients.
Subtraction (which is just addition) causes students trouble, usually because they forget to distribute.
Multiplication is generally easy, but can be tedious. Multiplying two 5th degree polynomials is time and space consuming.
Division is probably the hardest operation. It can be quite simple (if, for example, you are dealing with power functions) but can be very time consuming when dealing with polynomials, etc...
Composition can be quite easy to perform, but managing the domains of the functions can be challenging. (Not one of the four basic functions, but usually taught soon after basic operations on functions.)