The Russian Orthodox church and Greek Orthodox church are extremely similar. This dates back to 1472 when Ivan III married the last heiress to the Byzantine throne (and no doubt the influential relationship between the Byzantine Empire and Russia existed previous to this period). From this, huge amounts of culture were integrated into Russia from the Byzantine Empire such as a majority of "Russian" names... Alexander, Yevgeny, Demitry, etc, all of these have Greek roots. When I lived in Greece as an exchange student our горничная who was from Russia was describing to me all the similarities she saw between Greek and Russian.
For instance in Greek the second person plural verbal conjugation is EXACTLY the same.
Russian: вы понима
ете
English: you understand
Greek: eseis katalavain
ete
The second person singular verbal conjugation is also clearly similar to the Greek just with a little phonetic change. (The "ei" spelling is a Greek dypthong which is pronounced like Russian "и" )
Russian: ты понима
ешь
English: you understand
Greek: esu katalavan
eis
The language share a lot of grammatical similarities as well, and I wouldn't imagine either would pose much problems for either speaker. But I still find Russian much easier than Greek, maybe just cause I'm more passionat about it.