Vidu, miaj piedoj ne estas tiom malpuraj kiel la viaj.

It's not only feet that can be dirty.

A comparison could be made between the first child's feet and the second child's arms (tiom malpuraj kiel viaj brakoj). However, in using 'la viaj' it must be feet (the body parts already mentioned). I don't think that can be interpreted otherwise.

Miaj piedoj estas tiom malpuraj kiel viaj, is not so explicit and sort of leaves hanging what is being compared - to some extent invites the question 'my what?'.

At very least, 'kiel la viaj' is complete. 'kiel viaj' could be further specified, and to that extent is incomplete. Of course, common sense would tend to impose the same interpretation on 'kiel viaj as 'kiel la viaj' in this sentence.