It's long been believed that interceptors (small satellites that can maneuver) would be a better way to take down enemy birds. Electronic jamming can also be used to interfere with communications with a satellite. A laser is also limited to satellites that pass nearby. Moreover, satellites can be modified to make them more difficult for lasers to damage. It is believed the Chinese project is a result of China realizing that a major American vulnerability is its large satellite network. Thus any damage to U.S. satellites would have a larger payoff than if the money were spent on more conventional defense investments.
The U.S. has revealed that China's developed a powerful, land based laser, that has been fired at American satellites. This has apparently been going on for three years. In theory, a land based laser of sufficient power could damage some types of low orbit photo and radar satellites. No details on the effects of the laser attacks were given, as this would inform the Chinese as to how well, or not well, they were doing. The Chinese may have lasered some of their own satellites, as part of what is apparently a development project.