When should I enchant with Muffle instead of Sneak?

How Sneaking Works Internally in Skyrim

Internally, the game engine keeps track of a player's Stealth Points - you can think of this sort of like a regenerating health mechanic. Anytime an enemy has a chance to detect the player, the engine begins an ongoing series of opposed skill checks between the player Sneak skill and the enemy Detection Value. Any time the enemy wins, the player loses a certain amount of stealth points. When the player reaches zero stealth points, they are detected. Whenever the enemy loses, stealth points regenerate. When the player reaches full stealth points, the enemy is no longer aware of the player.

Detection Value

Detection Value is made up of:

• Enemy Base Sneak +
• Sound generated by the player * +
• Visibility of the player * +
• Enemy Sneak Skill *+
• Player Sneak Level Bonus

(Starred items have range modifier. Greater distance reduces detection chance.)

Here's the relevant points for how the skill checks are made:

Sound is the sum of Movement Noise + Weapon Noise

• Movement Noise is modified by how much weight you have equipped and what type of weight you have equipped. 5 pounds of Heavy Armor makes more noise than 5 pounds of Light Armor. Running makes more noise than walking. Sprinting makes more noise than either. Muffle enchantments you place on items eliminate Movement Noise completely (but loot which is pre-enchanted with Muffle does not!)
• Weapon Noise is created when you swing any weapon other than a dagger. Since you'll be using daggers, you can disregard this, as daggers make no noise.

Using daggers with a Muffle enchantment on your boots, Sound will be 0.

Player Sneak Level Bonus is Player Sneak skill - Enemy Sneak skill

Player Sneak Skill is modified by the total value of the all of the sneak modifiers available, and then compared to Enemy sneak skill.

It doesn't matter how much the player's Sneak skill is, only how much the player's Sneak exceeds the Enemy sneak. That is to say, a player with 100 Sneak will be detected by an enemy with 90 Sneak exactly as often as a player with 20 Sneak will be detected by an enemy with 10 Sneak, all else being equal.

Therefore, enchanting your boots with Fortify Sneak will increase your Sneak skill by however much your Enchanting bonuses provide, which might or might not matter depending on the skill of the enemies you're up against.

So just answer my question.

Fine.

• If you choose to equip items which weigh a lot or are classified as heavy armor, then take Muffle, to eliminate Movement Noise.
• If you have a very high Sneak skill relative to your enemy already, take Muffle.
• If you choose to equip items which do not weigh a lot or are not classified as armor, then choose Fortify Sneak.
• If you have a Sneak skill which is equal to or slightly less than that of your enemy, then choose Fortify Sneak.
• If you have a Sneak skill which is greatly less than your enemy, then you're screwed either way. Enchant the boots with Fortify Sneak, sell them, and use the gold to buy a carriage ride to a lower-level area where you can grind your Sneak skill up for a while.
• If you want to make a sneaky archer rather than a stabby rogue, choose Fortify Sneak. Sound is reduced based on distance, but Sneak skill is not.

Sources:

Bethesda Creation Kit: Detection
Bethesda Creation Kit: Stealth Points