Lanyue, which masses 26 metric tons, can land two (maybe four?) astronauts on the moon plus a 200 kg rover. Space X's Starship is designed to land 100 tons on the moon--that's 100 tons of payload.
Let's say you want to build a small moon base, one that's maybe 100 tons (ISS is 400 tons). How many Lanyue launches would be necessary? Maybe 10? Now remember that each launch is expendable. It will cost China between $500 and $1 billion per launch. That's $5 to $10 billion for a moon base, not counting the cost of the base itself!
Starship is designed to be fully re-usable. Their goal is to get each launch to cost $10 to $20 million total. To land 100 tons on the moon, they will have to refuel in orbit by launching between 10 and 20 tanker flights. That means one trip to the moon costs $200 to $400 million maximum. Even assuming that Starship underperforms and can only land 50 tons on the moon, we still only need two launches for a total cost of $800 million maximum.
That is literally 10 times cheaper than Chinese capabilities; alternatively, it is 10x the payload at the same cost.
Of course, there are two major developments that Space X still needs to demonstrate: rapid re-use (to bring the cost down) and in-space refueling. And that's why it's taken so long.
But if/when they pull it off, it won't really matter if China lands first. The American program is much more ambitious.
For the Chinese however this is their first rodeo.