The U.S. economy is nearly 2x larger than China's, and if you're counting the entire "West" (I'm guessing you mean Europe + US?), it's about 4x larger. And that's just looking at GDP; if you consider GDP per capita, the difference is even starker: the U.S. is nearly 7x higher. In terms of immigration, the U.S. has roughly 750x more inbound immigration than China [1], and the EU has similar numbers [2].
I don't think the numbers back up what you're saying here — they contradict it pretty soundly. In fact, the U.S. currently is (IMO stupidly) trying to prevent people from coming at all because it has such a huge volume of inbound immigration.