By and large they do. English, like all indo European languages, used to have many grammatical cases and verb forms. Now we mostly retain cases in pronouns, and most verbs are about two forms per tense.
Latin used to have all its cases suffixes, and today's Romance languages have dropped nearly all of them.
English has simple verb and noun morphology, but very complicated syntax and phonology. Hard to say that it’s uniformly more or less complex than Latin.
