The ability to handle voltage is dependant upon the dielectric strength of the insulation, or the distance from other conductors and grounded objects (like overhead high voltage lines which are only insulated by the air).
Stranded and Solid wire, as far as I know will both carry the same current assuming they are the same size in circular mils, and made of the same material. Once again, the makeup of the insulation also comes into play here, the ampacity tables in the NEC point to this.
Clear as mud?
