Classically a black hole made from collapsed matter would look (to people on the outside) exactly the same as a black hole made from collapsed anti-matter.
They would absorb things the same and the curvature outside would be the same so everything would orbit it the same way and get pulled in the same way.
What's interesting is the word black hole refers to the black event horizon not to the singularity that might be or form inside the event horizon.
So if you entered the black hole you might notice a difference if you entered early enough and had fast enough rockets to reach the surface of the collapsing object after it formed the event horizon but before it formed any singularities. The main difference would be whether it annihilates you when you reach the collapsing surface. And no one outside would know which happened.
Enter too late after the horizon forms and you can't reach the surface of the collapsing object before it forms a singularity in which case you'd have to ask whether different singularities act differently and to that we just don't know.
That was all classical with no quantum effects (outside no difference, inside a difference for sure if you enter soon enough and unknown otherwise). If you try to take quantum effects into account the quantum vacuum might be polarized differently around a recently collapsed star from antimatter rather than matter but it is speculative what happens so all that does is bring "I don't know" to a larger region, to the recent outside.
As for the speculative quantum interactions, if you were that close spatially and temporarily you were basically already interacting with the star as it fell through, sorta like you started an interaction with it that just hadn't finished yet as it crossed, so it's kinda cheating. And as you said in your comment you'd already be able to figure it out by looking at the highest speed things it emitted as it fell through. Also since there is some asymmetry between matter and antimatter you might even be able to analyze the light it emitted as it fell though. But that will be red shifted tremendously, so it's a bit like frozen star or red star analysis if you are familiar with those terms.