About 50% bonus to laser damage and 20% penalty to plasma damage. Laser rifles are slightly less effective than heavy plasma. even after those modifiers, though.
And yeah, random chance makes a big difference. Basically, any successful hit does 0-200% of the stated weapon damage (explosives are 50-150%), minus the armor rating.
So a shot against a high armor target like a sectopod is very likely to be a glancing hit and do no damage, unless you're using a high-powered weapon like the heavy laser.