Several points : The first thing you need to clearly define what your speaker do today and that you want the new speaker to do as well.
second you need to know well what your current speaker does not do and you would like the new speaker to be capable of.
Then you will probably do an analytical listening of the desired speakers to hear how they fit the bill .
And last and most important as ghdprentice wrote you need to just listen to music forgetting your analytical analysis .
Does this speaker draw you into the music, does it provide emotional connection to the music .
It is manadatory to hear these speakers with your amplifier .
As far as brand you will have as more advice as there is brand on earth as we have all different taste in what reproduced music should sound .
Myself a long time ago I used to have bw 802n with ar tube gear and then while abroad bw 805d with ar tube gear .
For a few years I went to Martin Logan montis but I came back to the electrodynamic speaker as the electrostatic can’t provide enough dynamic .
I have auditioned the bw803d4 and I did purchased them .They have been in my system for 2 months . I am very happy with the sound quality . My room is 350square feet .
I did also listened to the 801d4 ,they are fantastic .They have in my opinion excellent bass .
i did listened several time to the bw d3 série but never liked them . Much to hifi sounding . The d4 is just much more musical .