Briefly normal map (RGB - blueish) is better than bump map (greyscale). Bump map only contains ‘height’ info. Normal map includes ‘angle’ info additionally, so results are more realistic. The difference become more significant in ‘realtime lighting’ environments (when day-night time or light intensity or camera position changes).
Normal Map (Tangent Space) type is widely used and suitable mostly. Check this for a brief comparison: Object space, world space and tangent space. There says:
Object space is the local 3D space of the object. Up is always up and left is always left. It is a uniform space that you understand really well because that is what the world is really like. Tangent space, on the other hand, is best thought of as surface space. In tangent space, up is always away from the surface (in other words, along the normal). Left, right, back and forward slide you along the surface.
Also check this for a detailed information and comparison: Normal vs. Displacement Mapping & Why Games Use Normals
Vray 3 Manual gives little info about bump types too.
You can easily distinguish them visually:
Another 2 good articles (first one a bit old but worth reading): Creating and Using Normal Maps and Tutorial 13 : Normal Mapping
Lastly, i’m not sure why tangent space acts weirdly in your case. Please test with these 3D scanned materials to check whether it’s a problem in your generated textures or not.