The differences shouldn't be big. The BHSEs I have heard sounded very much like my BH- great control of the drivers and very high bandwidth. I know some people think they are bassy amps, I do not hear this. When the music has a lot of bass I can hear and feel the bass with the HE60 and O2. But say for example a lot of Blue Note jazz where Rudy Van Gelder often recorded the bassist further back in the mix, you hear the texture and depth of the bass but it is very soft and very much in the background. 
 
For example with my HD600/ EC HD300 wrt to the the Blue Note jazz the bass was often almost as forward in the mix as the rest of the instruments. This leads me to believe that either the electrostats and/or amp have more accurate frequency response or that the electrostats are far more spacially resolving.