I don't know about Bratislava/Warsaw and Moscow, but I can speak for Bratislava/Warsaw and Belgrade.
Actually, I just came back from a trip to the cities of Western Slavic states(Warsaw, Gdansk, Gdynia, Krakow, Zakopane, Prague, Karlovy Vary, Bratislava) and I will tell you right now, it was a little creepy how small the differences were. In Bratislava & Prague I felt like I was in Serbia(from peoples faces, to womans beauty and the quality of beer, everything was more or less same)
In Poland, where at first glance the local language seems the most complicated and different from Serbian (compared to Polish language, Czech & especially Slovakian are like dialects of Serbian or vice versa) , we realized that its not so different after all - its just that Poles apparently never had someone like our Vuk Karadjic to simplify their language a bit like we did
Few people in Poland speak english, but it didn't matter to my friends and me...we conducted most of our conversations in Serbian, from ordering food in restaurants to buying train/bus tickets.
We're more similar than some would like to believe. The common mistake people can make is confuse the silly politics of the day with the real & sincere situation on the ground.