Yes, Western militaries generally don't have unified command structures. Which is better? We'll see when the balloon goes up.
I think ours is better. Our services can fight for their unique doctrines and weapon systems, but they all practice joint forces operations. It is not unusual for some operations where all three services is under an admiral or theater commander (air or ground). If one looks at the PRC navy, its chain of command and programs is under Army control. Their navy is subservient to Army needs. That is good for local area power projection (i.e Taiwan invasion) but can hinder naval weapon system or projects that support an independent fleet doctrine, especially if these systems must compete against PLA ground priorities. Example would be long range rocket artillery or missile (Army force projection) versus naval offensive weapons such as all weather carrier based aircraft, missiles and etc. If they have the money for both, not a problem, but if they do not, the navy projects will be delayed in deference to Army needs because they dominate the higher ranks of the bureacracy.