Impressionistically, verbs seems to be as complex or more morphologically complex than nouns.
What are some good examples of languages, if there are any, where A) there are good diagnostics for distinguishing nouns and verbs and B) nouns have higher morphological complexity than verbs? (And, as a follow up, what's a good technique for measuring "morphological complexity" in this context?)
The best example I can think of off the top of my head is Tsez. Nouns appear to inflect, at least, for number and case, and many of the locative cases appear to consist of multiple morphemes.
The Tsez example is sort of borderline though because verbs inflect for the class and number of their absolutive argument (although not person) and verbs inflect for tense (which includes a two-way evidential split in the past), mood, and polarity. Tsez is not an unambiguous example of a language where verbs have greater morphological complexity (qualitatively) than nouns do in my opinion.