If you interested in studying of mechanical aspects of structures near to surface of cell then AFM is your chois. In same time CLSM could give you more information and better picture of intracellular structures and 3D distribution as well as.
I never found CLSM images in small (eg. 100x100 nm) scan size. CLSM is better for biological samples imaging. AFM works as 'stylus profiler" - i mean we have interaction of probe with the surface (and materials field), what gives us many possibilities according to measure differences in: hardness, elasticity, viscosity, magnetic force (attached file), friction, conductivity, electrostatic field, and so on. Moreover, AFM is measuring device, and I do not know if CLSM may be.
Talking about biological samples, CLSM gives the distribution of fluorescent-labeled proteins (or lipids and nucleic acids) and compartments inside the cell or at its surface. Functional probes can be used to measure intracellular pH, calcium concentration.
AFM gives physical measurements at the surface of the cell (topology, elasticity, viscosity...), but you can also get much deeper information like seeing the cytoskeleton or hard intracellular compartments through the plasma membrane. It is also possible to bind proteins at the tip of the cantilever to measure adhesion at the plasma membrane (ligand-receptor).
Finally, why used AFM instead of CLSM? It is also possible to do correlative microscopy, looking the same sample at the same time, with an AFM microscope coupled to an inverted CLSM microscope on fixed or live cells.