Encyclopedia Iranica, a fascinating website, has several long articles on the relationship between Armenia and Persia. This one in particular treats on ancient history and linguistics. The history section is as good a summary of Armenian history as anything I've ever read. It makes a bit more sense now...
Armenia was originally a Persian province. Old Persia, the Persia that the Greeks fought against, the empire that went from Asia Minor to Afghanistan--world-bestriding Persia. And something like 40% of Armenian vocabulary straight-up comes from Persian (fascinating!). Not modern Persian, though--we're talking Old and Middle Persian. Apparently linguists can look at Armenian for clues to what Persian used to look like. It's the common phenomenon of a colony being more linguistically conservative than the linguistic country of origin...cf. American vs. British English. (I'm not talking about spelling.)
It bears some similarities with English's relationship with French. A great deal of English vocabulary comes from French, but not the modern kind--it comes from medieval Norman French. I'm sure it was pronounced differently from the modern Parisian variety too.
This has been your Linguistic Interlude for Today. Stay tuned, another installment is sure to follow. :)