Dear,
I'm not a bryston engineer, but I know all the schematics of all the amps as the top of my thumb

The 7BSST shares the same amplifier modules as the 4BSST. In the 7BSST they are bridged. The powersupply rails are reduced from 85 volt +/- for the 4BSST to 65 volt +/- for the 7BSST. In this way more current is availible. Another difference is powersupply's capacitance. The 4BSST use 8x5600MFD elco's per amplifer. That make 44800MFD per amplfier.
The 7BSST use 8x10000 MFD powersupply capacitance. That make 80000 MFD per amplifer side, = 160000 MFD per channel! vs. 44800 MFD for the 4BSST
The 4BSST uses two 600V/A transformers. The 7BSST use one big one for both amplifier sides.
The 14BSST differs from the 7BSST in powersupply. At the 7BSST they use more smaller capacitor's together and they are close to the output section. That makes a fast powersupply. The 14BSST use 4 big capacitors instead of 16 small ones in the 7BSST. The 14BSST use 4x 27000MFD per amplfier. That makes 108000 MFD per channel instead of 160000 MFD for the 7BSST.
Also the 14BSST have a slightly lower powersuply voltage, 60 volts +/- isntead of 65 volts +/- for the 7BSST.
Resume:
Bryston 4BSST:
85 volt +/-
5600 MFD x16 supply capacitance (total: 44800MFD a channel)
Bryston 7BSST:
65 volt +/-
10000 MFD x16 supply capacitance (total: 160000MFD a channel)
Bryston 14BSST
60 volt +/-
27000 MFD x8 supply capacitance (total: 108000MFD a channel)
Conclusion.
The 4BSST can have a sligtly tighter bass, because it is a non bridge desing. The 7BSST and 14BSST are bridge design's and that halves the dampingsfactor. (output impedance get twice as high) On the other hand the slewrate doubles, so the amplfier can be faster.
the 4BSST have a common ground, also as return for the speaker. The 7BSST and14BSST are bridges, and the speakers float between the + and - amplifiers. This makes a real differential design.
The 14BSST sounded slightly softer in texture then the 7BSST. And i think that is the result in of different powersupply.
The 14BSST is a great amp but I prefer the sound of the 7BSST's
With kind regards,
Bas