During the Napoleonic period cossacks were generally not regarded as "battle cavalry" and rarely did much on the battlefield. Though is rough hierarchy of cavalry weight hussars, dragoons, cuirassier, there are many examples of lighter cavalry overthrowing heavier cavalry.
However there is vast range of other tasks required of cavalry in addition to performing on the battlefield. Scouting, pursuit, outposts, guarding prisoners, police functions in rear areas. The cossacks were used predominately in these functions, and with greater endurance, light supply needs ideal for many of these functions. While poor in massed charges they were adapt as small skirmishers particularly in rougher ground the regular cavalry could struggle.
Russian cossacks intros period took most of this workload off the regular Russian cavalry which meant they would be conserved and fresher for battle. Their raiding in 1812/13 greatly added to the french difficulties in supply , movement and rear areas with greater escorts needed. Small detachments of regular cavalry and horse artillery were attached to the cossack flying columnist give them a bit of punch.
Cossacks were also available in large numbers, and were relatively cheap to raise. Guard cossacks were different and had a good battlefield record.