I've had six laser sessions which (cumulatively) have cleared the overwhelming majority of facial hair I had. This has made a noticeable difference in smoothing and streamlining the shape of my lower face. Because I didn't have hugely dense growth elsewhere, the most notable effect for me has been on the upper lip area -- it no longer 'sticks out' like it used to. Overall, if you were to measure the difference objectively (numerically or whatever) I suspect it would be incredibly subtle... but the difference in perception is enormous. The combination of this with the absence of beard shadow has given my whole lower face a much more feminine appearance.
I haven't had electro yet so I can't compare -- and obviously neither can change the shape of the underlying jaw/chin in any significant way -- but laser done properly damages or destroys hair follicles and seals capillaries so that they can no longer grow hair. In other words, for those follicles it affects, it does the same thing electrolysis does but using a different medium (heat generated by the absorption of light as opposed to chemical electrolysis and/or heat generated by the absorption of radio waves). The only caveats are that laser at doses insufficient to permanently disable follicles may result in the eventual regrowth of those hairs, and that laser can't guarantee to permanently disable every single follicle in every area during a treatment (it's a more broad-brush approach, which is why it's so much faster) -- but otherwise the end result is the same either way.
