From my limited knowledge, Lab tools works in L*a*b* color space and the corresponding tools and curves in Exposure tab works in RGB color space. Lab color space separates luminance from chroma, so when adjusting lightness/contrast with Lab tools, the color is not affected. On the other hand, when you try to adjust exposure with RGB tools/curves, the saturation of colors will be affected. Adjusting Lab chrominance should have no effect on exposure but adjusting RGB saturation will affect lightness. The RawPedia should have a good explanation of the difference of both tools:
In practice I found that adjusting exposure with Lab tools will produce “dull” color and RGB tool doesn’t do that. I would just use lab adjustments when I think the saturation of the image is a little bit too much, or if I just want to keep current saturation “as is”. My 2 cents.