The correct statement is "I walk faster than John does." (or, possibly, "I walk faster than does John," but that's a whole other issue.) Comparisons have to be apples-to-apples; that is, the things you're comparing have to be similar or parallel. If you're comparing the way that you walk to the way that John walks, your sentence structure needs to make that clear. Otherwise, you could be comparing "faster" to "John." It's kind of hard to see how that could be in your example sentence, so let's take a different one:
I am more sensitive to criticism from Emma than Jenny.
This comparison is unclear; it could mean that I am more sensitive to criticism from Emma than to criticism from Jenny, or it could mean that I am more sensitive to criticism from Emma than Jenny is. We need to know which one it is, so we make that sentence either
I am more sensitive to criticism from Emma than from Jenny.
or
I am more sensitive to criticism from Emma than is Jenny.
Basically, your goal is always clarity, and if that requires one or more extra words to make a comparison explicit, then put those words in.