I watched both shows and I never made the connection until you laid it out. They core themes are remarkably similar.
I would say though, that women were better represented in Living Single than the were in Friends. For example, Regina's analogue, Rachel, was defined by men… by her need to be married, by her obsessions with men's attentions, etc. for most of the first half of the series. However, Regina was never defined by men's attention; rather, that attention was an accessory of her persona.
Max was my favorite character on Living Single. Chandler was my favorite character in Friends.