BaK4 glass has a higher refractive index than Bk7. In other words, BaK4 tends to refract light more strongly than Bk7. For bin prisms, this means that incoming light can hit the BaK4 prism at a steeper angle and still achieve complete internal reflection within the prism. For a Bk7 prism, it can still achieve complete internal reflection, but only for light rays that are hitting it at a more shallow angle compared to the BaK4 prism. In the Bk7 prism, if some light rays are coming in too steep (like from the extreme edge of the objective), then you will only get partial internal reflection from those areas of the objective.
If you look at most porro bins these days, it looks like their objectives are relatively "fast", maybe around f/4 or so. At f/4, light rays from the edges of the objective are coming in to the prisms at a pretty steep angle, and so BaK4 glass would be better than Bk7 if you wanted full illumination of the edges of the exit pupil. If you paired Bk7 prisms with such fast objectives, then you'd get the familiar diamond shape exit pupil. I've attached a picture of this (sorry, not the greatest picture). If you were a binocular designer and wanted to get those edges fully illuminated with Bk7 prisms, you'd probably have to use a "slower" objective and extend the optical path considerably, so that the lights rays from the edges are hitting the prisms at a more shallow angle. But this would make the overall bin less compact.
In bright light, when most people's pupils will contract to may be 2 or 3 mm diameter, using a bin with Bk7 prisms might be just as good as one with BaK4 prisms because you might be able to center your pupils within the fully illuminated section of the bin's exit pupil. The semi-illuminated edges wouldn't even matter. However, in low light, maybe the dim edges would be more noticeable. Personally, the only reason why I'm a bit careful about buying modern bins with Bk7 prisms is that it makes me wonder where else the manufacturer might have cut corners in order to drive down the production cost. Having said this, my first pair of bins from when I was a kid used Bk7 prisms, and I never had a problem with those.
