Was Cossack cavalry ineffective relative to other troops?

The Cossack cavalry was a light cavalry, acting mainly with raids against logistics, hit-and-run tactics against moving portions of armies (for example the Great Army when it was retreating) and scouting for the main army (for example the attack on Napoleon just before Austerlitz).

In all these roles, Cossack cavalry was as effective as other Russian light cavalries, as well as French cavalry.

It depends on what you are doing. If you line up a brigade of Cossacks versus heavy cavalry in a battle and charge both, the Cossacks would be wiped out. If you had the same brigade of each trying to control the areas around the two armies in the field, the Cossacks would run rampant over the area and the Heavies would be useless and vulnerable.

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.

Both sets of statements are true: The Cossacks were inferior to other types of cavalry, and the Cossacks were "effective," because they were good enough to do the job.

To take just one example, the cuirassiers were the most heavily trained, heavily armed cavalry around. That means that there were relatively few of them.

The Cossacks were the opposite: They were "random" soldiers drawn from nomads and "runaways" of the borderlands between Russia and modern Kazakhstan. Compared to other forms of cavalry, they were lightly armed and poorly trained. But there were a lot of them, and they were "handy" to have in tight situation.

For instance, Cossacks were instrumental in executing Peter the Great's "scorched earth" strategy against Charles XII of Sweden (whose troops were elite).

How and why did Charles XII Get to Poltava?

The Cossacks weren't great soldiers. Not really good enough for battles. But (barely) good enough to conduct raids and get a lot of (dirty) jobs done, meaning that they were "effective."

1. Cossacks in early 18^th Century were the light cavalry. The lightest one. Even Hussars needed carts with grain and food. But Cossacks used them only if it was absolutely impossible to “take” everything on site. So, they were very, very quick. Yes, in battle, they were weaker. But they were not meant for the battle lines, but for intercepting on the enemies communications. For this work they were formidable.
2. It is senseless to speak of Cossacks without mentioning the epoch. In 16^th or 20^th centuries everything was very different… There were no dragoons, for example in the 16^th Century, and Cossacks were instead. And Cossacks in the 20^th Century were very different, too. They became very multitarget.
3. All the time Cossacks worked also as saboteurs, as special regiments, and that role only increased in time.

Ineffective? No. Bruce Lee is weaker than a tank… Sometimes.