Indeed, for example, the BA is FULLY BALANCED, in and out, while the 4-45 has balanced outputs, but only RCA inputs !
is this a drawback or it does not make any SQ difference ?
It's more like a tradeoff. The BA does take balanced inputs, but the balanced inputs are converted to SE via transformers (those two small cylinders marked Cinemag mounted on the back panel of the BA). This is both good and bad. The good is that both legs of the balanced output are actually used. The bad is that we are adding an unnecessary reactive component in the signal path. Some DACs which have balanced output capability, electically sum the balanced signal for the SE output. So in this case, using short (not 30ft. length in studios) patch cables, it shouldn't matter on the 4-45. Other DACs, like the PWD2 I had, sort of cheat and simply use one leg of the balanced for its SE output. Taking the PWD2 for example, I felt the SQ was kind of a wash between the SE (one leg of the balanced) and balanced outputs into the BA. Really too close to call. It's important to understand that the BA is still a SE amp.
If you wanted to, you could wire up or have Craig build you a balanced to SE transformer box, but honestly, and depending upon the design of your DAC, it could be a waste of money as good transformers, even small ones, are expensive.
So I wonder if the 4-45 is just a more powerful BA that is useful only with very hard to drive headphones or... does the 4-45 sound better than the BA with ALL headphones ?
Taking out of consideration for any preference toward specific tube types, the 4-45 sounds better than the BA with all headphones across the board in terms of resolution, macro-micro dynamics, layering, separation, clarity, imaging, realism, and immediacy. It's hard to put into words, but "REAL" factor is definitely there, especially now that I've got the complement of tubes in there that I want. The 4-45 is a step up in driver control from the BA when it comes to orthos, but is still a step behind compared to the best solid-state.