I would use “as below” when the following explanation was a detailed paragraph or maybe longer. This would be a more formal way of setting out your statement  

The answer depends on context. "Follows" is the third person singular form of a verb. "Following" is probably an adjective, but could also be a noun or an adverb. "Below" is probably used as an adverb. You can use any word you want, but be aware how you use it. For example, if you use "follows" then you really should give it a subject. An active verb needs a subject. It would be better to say "as it follows". If you use "following" as a noun then "as following" makes no sense. You would need to say "as in THE following". If you use "following" as an adjective, then give it a noun to describe: "as in the following paragraph". "As below" lacks precision. Below what? As what below? An adverb like "below" needs to modify something. What does it modify here? I would say "as seen below", "as shown below", "as explained below", or something like that, so that "below" modifies something. You can omit such details if you want and ignore grammar. People do say things like "as follows" with no subject. It won't get you in trouble because people will recognize what you say as a sort of abbreviation. However, if I were learning English then, for now, I would strive to follow all the rules. You can break them later if you want.

I don't think there is much difference, except the information would definitely need to be below for the second option.