The source is the most important and fundamental difference.
An optical microscope uses visible or near UV light as its source. The wavelength of the photons is the resolution limiter. Diffraction-limted systems (90 percent of all light microscopes), have a maximum resolution limit of 200-300nm. This is with state-of-the-art optics.
An electron microscope uses electrons to source (FEG) in modern SEM/TEM. These electrons are accelerated to very high energies – up to 30 kV for SEM and 300 kV for TEM.
This yields a very short wavelength for the primary electron, 2.5 pm at 200 kV acceleration voltage.
Our resolution limit does not depend on the wavelength of the source, but optics imperfections (mainly spherical or chromatic abberetions). Modern SEMs have a resolution of 0.7 nm, while uncorrected SEMs are about 1 A.
Current Cs and Cc corrected TEM Resolution Record is 50 pm.