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Due to their high speed and ranged attack, Cavalry Archers make an excellent harasser, hit-and-runner, and a good counter for infantry units. With enough micromanagement, a small force of Cavalry Archers can take out whole contingents of foot-soldiers. They also possess very solid stats all-around, so they fare well even when caught in battle.
However, they are hindered somewhat by their high attack delay. Their armor gets upgraded through the archer line, but in terms of attack bonus against them, they count as botharchers and cavalry.
However, Cavalry Archers require many technologies to be researched to make them effective, meaning it is difficult to get a group of them out in a reasonable timeframe without them being weak. Additionally, they are countered very cost-effectively by Elite Skirmishers, which Cavalry Archers generally cannot outrange, as these can soak up the damage from Cavalry Archers, and deal drastic bonus damage to them. Mangonels and Scorpions can also be devastating to a group of Cavalry Archers if they don't avoid their projectiles, while rams can be used as a very effective damage sponge against them.