Illustrator brushes can only be AI files, since only AI files can contain all those AI-only features.
If they are EPS files, you need to be at least cautious. Some EPS files might contain an AI file in them, which can also have brushes in it. But the basic EPS file can only contain the shape you can then use to make a brush of, but not the brush itself. PNG files can of course also be made into a brush, but that is even more work and you will need Photoshop (or the like) in addition to Illustrator.
The first split point starts at the Vector and Pixel point. Some illustrator brushes have a pixel look and effect. Bristal brush is one of them.
In general this is not possible. But for some visual effects, trials can be made for similar effects. For brushes with sharper lines. Especially illustrator brushes can be transferred to Photoshop more easily. This is a subject open to development.