I'm late to this discussion, but here is my video if you have not seen it comparing my slant top 4x10 to the BF 4x10. The speakers/drivers from the slant top were installed in the BF so the difference you hear is purely the cab. https://www.youtube.com/watch?v=7xcCaacIxdk
I think from this you will understand, that it comes down to how full is the range of tone the cab is producing. I think the BF allows any amp to have a broader range as the cab put out a fuller range. However, as I note in the video, if you are going for that classic mid range tone and nothing else, then the traditional cab with a driver bolted to a flat board recessed enough to protect it is it.
The only cab I have heard that came close to the tone ability of the BF was my old Ampeg V2. They were a ported cab 4x12 with the cab divided into a 2x12 configuration. I have a video up of that too, though my playing is just plain goofing off. Here is the V2 video if interested: https://www.youtube.com/watch?v=hTtyGMoN4JA
I have run tubes and transistors. I still have my first amp 69 Fender Princeton. My second amp, a Peavey Musician Mark 3. People are amazed at it's sound. It actually sounds like it warms up as a tube does. I sold the Ampeg V4 as it was just too much to move. My primary amp is a Peavey Classic 50 head into the BF cab. I have also used the Princeton at a few gigs, though not into the cab. I changed the speaker in it in college and it woke up the amp. I know people would think it was blasphemy to dump the original speaker, but really it sucked.
I forgot, I have a 76 LP, black custom with a maple finger board. Bought it new. I tried the gold and sunburst, but this was the one that took off in harmonic feed back at the same volume I tested the other 2 at which was a good thing as I wanted a black one.