In a thread on the Adobe ACR forum the late Bruce Fraser wrote:
"When you boost exposure, you're stretching the entire tonal range.
When you boost brightness, you're stretching the tonal range between the shadow and the midtone, and compressing the tonal range between the midtone and highlight.
Because cameras capture photons linearly (they don't have the compressive nonlinearity offered by eyeballs or film), you have a great deal more data in the midtone-to-highlight range than you do in the midtone to shadow range.
So boosting exposure and lowering brightness stretches the data-rich highlight range and forces more bits into the three-quarter and shadow regions, where you need them. Leaving exposure alone and increasing brightness stretches the relatively data-poor shadow to midtone range, increasing the likelihood of posterization, and making shadow noise more obvious."