The thing is carbon nanotube muscles can't be used by tanks, or any other wheeled vehicle. It's a linear actuator rather than a rotational actuator. Wheels need constant rotational motion to move, and CNT muscles can't provide that. They simply contract like biological muscle, although much faster and with more power. CNT muscles are so incredible it would be foolish not to use them, and the only way to do this would be to have a walking machine. They are 1,000s of times faster and stronger than biological muscle, they use very little power (they can be made to trigger using body heat or sunlight), they are very light, weighing only as much as the wax that they're dipped in, and they're performing research on giving it the ability to "heal" itself. A tank's locomotion system (it's engine, radiator, transmission, etc.) weighs many tons, but this would be replaced in a mech by CNT muscles that altogether would weigh less than 1-2 tons. This extra weight could be used to cover the mech, which would have about the same surface area as a tank, and wouldn't need as much anyway because the CNT muscles would act as its own armor.
Here's a picture I drew up a while back to show the size/surface area comparison of a mech and a tank:

This one shows the tank's side profile better:

I play War Thunder so I know how well you can protect yourself by using proper technique, but mechs can also use these techniques. However, I believe mechs would benefit in an urban situation. (Pardon the crappy picture)

When a tank takes cover behind a building in tight spaces, it's going to be about perpendicular to the edge of the building so that it can dart in and out. Tanks can do this pretty quickly, but they still expose a large portion of their surface area before they can even fire. They mech on the other hand, exposes very little of its surface area since it is more vertical than horizontal.
I think that mechs will be more of a walker type than a humanoid type. Arms don't really make sense. It would be more beneficial to have a tank turret on legs. A mech may not be able to go hull down in as many positions as a tank could because it is slightly higher, but the mech can also crouch, meaning it can pop up and fire much faster than the tank can drive up the hill, fire, and go back.