An exhaustive list of words in any language is troublesome to impossible to make because of dialectal differences, English not having a regulatory authority like Spanish does (and even with Spanish there are slang words that the RAE doesn't recognize), and so on.
The DRAE consists of 83,431 entries (source), while Webster's Third New International Dictionary Unabridged has about 470,000 entries (source). That's a little less than six times as many words, although it should be taken into consideration that there are many regional dialectal and slang words that the RAE is not recording.
As for vocabulary, SpanishDict claims that the vocabulary of the average Spanish speaker is 10,000 words, but simple conversation only requires 1,000. For English, a question on Amazon's Askville cites a study that claims a conservative estimate of the vocabulary of a college graduate is around 20,000 words, and an ESL company claims that 15,000 words should be enough to read 98% of texts and that 3,000 words would be enough to get by on at minimum.
So, while English might have many times more words than Spanish does (or at least the "official" version that the RAE records), the vocabulary for English is on the whole much larger. That doesn't necessarily mean that Spanish is less "expressive", though; while it certainly might be more verbose sometimes, people will always find a way to say what they want to say, and they'll coin a word if they don't have one to use. (In fact, English's judicious use of loanwords might be one reason its vocabulary is so massive.) And all languages are constantly changing as the people and culture changes too, so in a few years it could very well be that the information provided here is outdated.