There is a subtle difference between the "Film" exposure setting and the CM panel exposure setting that may elude many folks.
The "Film" version, while functionally equivalent to the CM version (IE 2^EV_adjustment * scene_referred_render_value), is applied on the data. In the colour management panel, on the other hand, it is applied purely on the view.
If you are rendering out to display referred imaging encodes, such as JPEG, TIFF, etc., in all instances the impact will appear identical as the data is baked into the display referred format, with all view transforms.
However, if you save as a proper image pipeline format such as EXR, you will see the difference. In the case of the Film variant, the exposure adjustment ends up baked into the EXR's scene referred data. In the colour management variant however, being only on the View, the EXR will bear the original scene referred values as present in the direct render. If you save both versions, only in the latter will the data be saved at its original exposure value, while the former will actually adjust the encoded data.