The languages with the most words are probably fairly unknown tribal languages spoken by few people. Australian Aboriginal languages for example tend to be far more specific than English, dealing more with particulars than with generalisations.
When we get into polysynthetic languages we run into that nasty question: What is a word? Is, for example, old-male-goanna-with-one-toe-missing-on-its-left-front-foot-and-scratching-its-head with-its-right-hind-foot-while-sitting-next-to-the-stream-that-flows-only -during-the-occasional-rainy-season one word?