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Linear Vs. Logarithmic Control
LFO SpeedLinexponential
Modulation AmountLinexponential

Note: These files are created by using a sequencer to send out the same CC# clip of linearly increasing control from 0 to 100 over a constant time.

Try opening these files in your favorite wave editor to both visually and audibly observe the rate of change curve.
In the case of volume, at half of the file, the linear volume change sounds to us like it is more than 50% of the maximum volume. The exponential volume change sounds more like it is actually 50% of the maximum volume at half of the file.

For the LFO Speed, observe that at half of the file the linear speed change sounds already too fast to tell the difference from half of the file and four fifth of the file. But the exponential speed change, at half of the file, doesn't. As a result, you have a wider useful range of sound shaping possibilities (especially for vibrato or tremolo) in the case of exponential speed change.

Anyhow, I think the most crucial downside of using linear change is in applying modulation amount. All though both linear and exponential change their values over the same range of modulation amount. The linear one appears to sound much coarser than the exponential . I think we miss out out a lot of subtle ranges if our synth can only apply the modulation amount in the linear fashion.

What made me think about this fact was when I tried to recreate this patch that I had created on the Virus on the uQ. (Essentially, the patch is nothing but 2 detuned saw waves with lfo modulating the cutoff of a lowpass filter with just a little hint of resonance.)The uQ modulation amount was too coarse to modulate the cutoff in the same range. Also there was no similar speed setting for the lfo, it was either too fast or too slow. By the way, I am not trying to trash the uQ here. I guess it just wasn't built for me. The uQ is probably great for loud and harsh sounds because its modulation and parameter ranges, that appear to be more linear than others, have more effect possibilities in the extreme side (rather than the subtle side). I just have no use for those types of sounds.