Well....
The Chinese are far more open than the Soviets were 40 years ago and I'm unaware of any construction of a large rocket for the Moon.
An asteroid mission will take much longer than a Moon mission only because asteroids are not in orbit around the Earth but around the Sun. A mission length induces all kinds of cumulative problems. And asteroids have such a weak gravity, astronauts will have to hook themselves (if it even works because of the dust that can get loosened when trying to hook) and beware of floating dust under such weak gravity!