According to which method of counting?
Wikipedia says [1] that "One most recent 2016 study shows that 20-year-old English native speakers recognize on average 42,000 lemmas, ranging from 27,100 for the lowest 5% of the population to 51,700 lemmas for the highest 5%." and "For native speakers of German average absolute vocabulary sizes range from 5,900 lemmas in first grade to 73,000 for adults."
In general, I'd expect all languages to have roughly similar vocabulary sizes, since they are mostly limited by the ability of native speakers to remember them.
[1] https://en.wikipedia.org/wiki/Vocabulary#Vocabulary_size