The main verb of the sentence is "work." The predicate (or verb phrase) is "work well at preventing serious illness but less so at stopping COVID's spread." However, the sentence has some complexity both in the subject and in the predicate. The writer is using formal style as well as being quite economical in making this statement. The predicate is a compound predicate: it consists of two predicates/verb phrases joined by a conjunction (but): 1. "work well at preventing serious illness" (but) 2. "work less well at stopping COVID's spread" Additionally, the writer has (i) elided (left out) the verb "work" from the second verb phrase because it can be inferred from the first one, and (ii) substituted the the adjective "well" with "so" in the second verb phrase (this is a characteristic of formal writing): 2a. "work less well at stopping COVID's spread" 2b. "____ less so at stopping COVID's spread" With regard to the subject (China's vaccines), we see more elision--the word "vaccine" has been elided, since it has previously appeared ("the West's vaccines"). If I were to rewrite this sentence to avoid the elision and make everything as clear as possible (while still using natural English), I would use do-support and write the following: "The West's vaccines work well at preventing serious illness and so do China's vaccines. However, China's vaccines work less well at stopping COVID's spread."

Please allow me to comment. The main verb is "work". The subject is "China's(vaccines)". So, predicate is "work well at preventing serious illness". "but less so at stopping covid's spread." is dependent clause. Which means does not have subject and verb. However, "but" is coordinate conjunction, main clause would be "China's work". I'm not native, If I mistook, I'd be sorry.

"At preventing serious illness " is the predicate verb.