The first comprehensive theoretical investigation of a series of functionalized fullerene cations, {R-C(60)}(+), where R = H, CH(3), CH(2)Cl, CHCl(2), and CCl(3), is accomplished. A detailed consideration of conformational energetic profiles of these systems resulted in the structures of most stable conformers that fit all available experimental data. The trends in stability of {R-C(60)}(+) cations as well as transition barriers for migration of alkyl groups over the C(60)-surface are provided. A thorough study of energetics of {R-C(60)}(+) is augmented by in-depth investigation of their electronic structures and aromaticity. As the final part of this study, the detailed comparison of structures, energetics and properties of {R-C(60)}(+) with those of corannulene cations, {R-hub-C(20)H(10)}(+), is performed at the same level of theory. The similarities and differences between the surface functionalized ball- and bowl-shaped carbocations are illuminated.