BK7 is the normal crown-glass for lenses and prisms. (K stands for the German: Krone) It has 7% lead-oxydants. High performing optical glass.
BK9 is als so used for lenses, chandeliers, jewelry etc. Less dense, high clarity, but as a result less capable of withstanding wear. So not as well suited for a front lens or use in a dishwasher. Common name: Crystal. 9% lead.
BAK4 ( Barium Crown) with slightly higher refractive index than BK7 has better capabilities for total internal reflection of rays at steeper incident angles in short focal systems like binoculars. So it is better in avoiding a bit of light loss.
One can see if binoculars has BK7 or BAK4 prisms by looking at the exit-pupil. BAK4 pupil is round, BK7 has a bright square.
Looking in the daytime with a 10X50 one sees no difference. The human entrance pupil is 2 mm, exit pupil is 5 mm. The slightly darker edges of the BK7 exit-pupil are vignetted by our own eye-pupil.
By night, with an eye-pupil of 6 mm for instance, one might expect to see some difference. Mostly this is not the case. A light-drop of 40% at the edge of our field of view is almost imperceptible to most people.
Advertisements in which BAK4 and BK7 prisms are compared you might notice a slightly darker BK7 image in the center. A difference that doesn't exist, only in the advertisement.
So what are BAK4 prisms good for? I imagine theorists, perfectionists and salesmen? It is better for nature though, for it contains only 4% lead. A salesman would say 50% less lead!