A solution is a mixture of a solid component called the solute and a liquid component called the solvent. Crystallization is the process by which the solute is formed into solid crystals and separated from the solution. Evaporation is the process by which the solvent is converted into vapor, leaving the solute component behind. Evaporation is a heat absorbing process requiring energy to take place. Crystallization occurs by letting a heated solution cool and letting formed crystals drop off.
The better method would depend on the solution. Generally, crystallization would be better when a solution is saturated but would be less effective if the solution is dilute. Also, solutions containing solvents such as acetone or ether, which evaporate at lower temperatures, would be better separated by evaporation than solutions containing water as solvent which evaporates at a higher temperature.