From Bialystok’s overview paper Bilingualism: the good, the bad, and the indifferent: “It is now well documented that bilinguals generally control a smaller vocabulary in each language than monolinguals” (2008: 4). Specifically, she cites a number of studies showing that this is the case for children. For bilingual adults, most of the results she cites relate to lexical retrieval (difficulty in accessing vocabulary) rather than vocabulary size per se.
A caveat: multilingualism research is a fast-moving field which i am not an expert in, and it could be that the consensus has changed since 2008.