I can't really give a straight answer (as you'll see, the pun is somewhat intended) on what it would be like of two black holes crossed paths. Known as a binary black hole system, the two black holes do not necessarily have to be the same size (though it would probably help the math a little bit). The math behind black holes involves something called geodesics, which can be thought of as math for curved surfaces. The first geometry you learn occurs strictly on a plane; this is known as Euclidean geometry. Astrophysicists use a generalized version of this. While I cannot adequately tell you what would happen, I can show you. In an article from just a few months ago, article some researchers calculated what two merging black holes might look like using different spacetime paradigms. If you look through the images, you can see that merging two black holes distorts space in pretty weird ways. Very little is known about what would happen, but it is generally agreed that the merging of two black holes would produce a massive amount of energy that produces ripples in the spacetime continuum, known as gravitational waves. We have yet to observe this.

It also turns out that the idea of black holes may need rethinking. The notion of black holes emerges from Einstein's theory of General Relativity. However, there might be inconsistencies with quantum mechanics and the conservation of information (which is essentially energy). The idea of what a black hole is and what it does is still a very open area of research and intrigue. You can read more about it here . There is also a pretty nice introductory article in Wikipedia article in wikipedia that gives an overview without too much of the math. I also recommend watching Cosmos with both Carl Sagan and Neil deGrasse Tyson. They are really quite rewarding, if not just for the black holes but also universe in general.

Hope this helps!
Best,