It has different information. You get additional spectral information, but you typically also lose a bit of spatial resolution because dye clouds are typically larger than the metallic silver would be from the same bit of halide.
Note also that many films have more than 3 sensitive layers, e.g. a second green layer with different sensitising dyes and different couplers.
B/W film has several layers not a single one at least if it is a panchromatic film, furthermore a lot of information gets bleached away during development of color film (all the silver). So a good B/W film has usually more resolution than a good color film. Color is an additional info but since B/W has more resolution it has more overall information compared to color film. I nearly forgot panchromatic film B/W has the same spectral information as the average color film (Fuji fourth layer is the exception) it just lacks the color projection filter also known as dye layer.