The problem

Benefits of using ModuleScope and Scope (instead of Module and Block):

• Not necessary to add new variables at the top of the block, i.e. Module[{variables...}, ...] (especially annoying in large functions).
• Changing variable names is simpler (again because you don't have to rename the names at the top).
• Merging and splitting functions is easier as it is not necessary to merge and split their argument lists.
• No performance cost as these functions are (macro) expanded at definition time.

However, as @maxitg said:

... we still want to use Module in pattern rules (e.g., {{a_, b_}} :> Module[{c}, {{a, c}, {c, b}}]). ModuleScope is undocumented so we cannot expose it to users.

Examples

You can use MacroExpand to see what these functions do:

In[] := MacroExpand[foo[] := ModuleScope[
   a = 1;
   b = 2;
   c = 3;
]]

In[] := MacroExpand[bar[] := Scope[
   a = 1;
   b = 2;
   c = 3;
]]

Comment

It is not simply a matter of replacing all Module's with ModuleScope's. See:

In[] := MacroExpand[{x_, y_} :> ModuleScope[{x, y + 1, z}]]

You can use ScopeVariable to "cause particular variables to be localized":

In[] := MacroExpand[{x_, y_} :> ModuleScope[ScopeVariable[z]; {x, y + z}]]

But it may not be worth replacing them in these cases.