They don't necessarily have MORE armor. But they can have massive wedge-shaped armor in the center of their torso, right in front of the pilot - something the tanks cannot afford, with the need to shield multiple crewmen. (think
Vulture, but with the pilot in the centerpiece rather than on top) With the main power source being right behind the pilot, there is little else that can be taken out with just one hit that would immediately cripple the mech. This is, of course, assuming a frontal assault. A side assault presents a different problem for a HEAT shell - the arms of the mech are likely to absorb the hit and the mech will suffer little actual damage.
You should also consider the myomers themselves. The material they are made of is likely to posess enormous tensile strength. A mesh of myomer fibers would thus provide additional protection from conventional armor-piercing weapons.
ninja edit: a multi-ton infantryman will, of course, sink into the ground, but it can be alleviated with a different foot design, and won't constitute a problem until the mech reaches a certain size. Twenty-five tons standing on a square meter of foot area would make
2.5 kilograms per square centimeter, with up to 25 kg/cm
2 at maximum stride. Not all that much, I think. I could be wrong though.
The armored fingers might not be as small and nimble as human ones, but they do have the bonus of possible cameras on their tips, not to mention any built-in arc welders, hacksaws, and dispensable foam sealant.
With a damaged foot, a mech wouldn't run, but would be able to walk at a normal pace, like a human with his lower leg in a cast would. With a missing foot, it would limp quite a bit, but would not lose mobility so much as to be unable to get into cover. Don't forget, a robot feels no pain and does not bleed, so it wouldn't be affected by limb loss too much.