The Composite Bowman is better than the Improved Bowman. Civilizations that can train the Improved Bowman usually have the ability to upgrade them to a Composite Bowman. Because of this, the Improved Bowman never really makes their full appearance in a random game. Boasting solid overall stats, the Composite Bowman is an excellent ranged choice due to its low cost.
Originally, Composite Bowmen were called Longbowmen, this is also the reason why their bow is longer than a traditional composite bow.
The Composite Bowman in game will not be able to imitate his pose in the icon. In the icon, he is facing southeast while aiming at an enemy, holding the bow with his right arm and arrow with the left, allowing his back to face the player's view. In-game, when he is asked to face same direction and fire at an enemy unit, it is the other way around, exposing his front view to the player instead.