Stranded and solid wire both have the same ampacities, as long as terminations are listed for the class of stranding that applies. Class B and Class C stranding are the most common, and most terminals are rated for this. Any higher class of stranding may need special terminations, or termination adapters.
In terms of voltage drop, for DC it makes no difference. For AC, the more strands of wire there are, the higher the effective resistance because of inductive effects.
In terms of ease of work, stranded wire is more flexible due to strands being able to slide past one another, and therefore easier to install in conduit. Solid wire imposes the rigidity of copper on the mechanics of your wire pull, which can damage the insulation integrity if you aren't careful. For lay-in wiring methods instead of pull wiring methods, the rigidity isn't as much of a problem.