What is absolutely astonishing, however, is how similar they sound, at least in terms of prosody. To my Hungarian ears Finnish, at least if heard from distance, sounds eerily familiar.

Compare this to e.g. Spanish and French, languages so close to each other but sounding so different. I wonder if there is some deep reason why prosody is well conserved in the Finnish-Hungarian pair and apparently entirely meaningless in Romance.

In terms of words or grammatical structures?