When I went looking for posters from the two different time periods, I found it much easier to find posters from right after the Bolshevik Revolution. The picture I found (on the left) is from the 1920's, and I'm not exactly sure the specific topic of the poster, but my guess is about politics. It's very easy to see that a grid was used with a small color palette. To me, the poster is almost intimidating with seriousness and the eyes looking slightly off to the left.
Now when I went to look for more contemporary work, I felt as if I were coming up short. I did find a couple pieces on AIGA's website. The one I am showing (in the red) is actually a book cover done in 2006, but looks like it could pass as being done as the same era as the other poster. The book is a classic novel that tells about times under Stalin. I was surprised to see how similar the designing was. It still follows a grid and uses similar typefaces for some of the information on the front cover. To me, it seems as if the Russians found a design style that really worked for them and stuck to it, making only minor adjustments. It makes it very easy to pick out Russian work, discuss and compare it stylistically as to what was going on during that time period.
sources: aiga.com; typogabor.com