Quick Answer:  A good well fitting, soft grazing muzzle is best.  When you use strip grazing the horse dives on the new grass and eats it.  But this still leaves him the "already eaten"  part of the field to munch on, often there is a lot.   However a grazing muzzle restricts the amount of grass wherever he eats.

A horse nutritionist came to look at my field, Skye was being strip grazed and only had a tiny amount of fence move.  She then moved on to the rest of the eaten grass which to me looked like absolutely nothing. 

However, Skye's nutritionist,  https://www.yourhorse.co.uk/author/donnacase/ who is very highly regarded, said - "Oh yes, there is plenty of grass there, if their head is down eating, there is grass"

So you can't rely on the eaten sections of field not being bare even if you think it is.

A grazing muzzle means they can only eat sparingly whatever the field offers so if your horse is putting on weight, be suspicious, they are getting calories from somewhere.