I did both of them back in 2011 whilst my brother-in-law was working in Moscow. By car (I borrowed my B-I-L's chauffeur for the day) the trip also took about two hours because central Moscow is so congested with traffic. The train sounds like a good option. The battlefield visit was excellent.
Both museums, surly babushkas not withstanding, are well worth a visit. I didn't like Moscow much (plenty to see but not very welcoming), so I'm glad I got as much in as possible. I might go to St. Petersburg in the future, but Moscow is not on my 'see again' list.
As said the Great Patriotic War Museum is also well worth a look. The tank park outside (almost on a different site and not that well signed) is packed with interesting stuff, including lots of lend lease kit.



