Double-duty quine: quine!dlroW ,olleH

JavaScript (ES6), 42 38 bytes

f=_=>/\//g&&"f="+f||"!dlroW ,olleH">=_

Reversed

_=>"Hello, World!"||f+"=f"&&g//\/>=_=f

Explanation

When reversed, it becomes an anonymous function that returns the string Hello, World!.

The regex /\//g becomes a comment when it is reversed, which allows the syntactically invalid >=_=f to be commented out in the reversed code.

Y, 19 bytes

Upxp"!dlroW ,olleH"

U captures a string with U at the beginning until the next U is met, in this case, the source code. p prints the item, and x is a termination link. When reversed, this looks like:

"Hello, World!"pxpU

This captures the string and prints it with p, again terminating the program with x.

Try it here!

JavaScript (ES6), 71 bytes

trela=a=>alert("trela="+trela+"\ntrela\n``")//
`!dlroW ,olleH`
trela
``

How it Works:

Line 1 defines function trela that when run outputs the program's source code. Line 2 is an unassigned string, does nothing. Lines 3 and 4 call trela abusing the template string syntax.

Reversed:

``
alert
`Hello, World!`
//)"``n\alertn\"+alert+"=alert"(trela>=a=alert

How it Works:

Line 1 is an unassigned string, does nothing. Lines 2 and 3 abuse the template string syntax to print Hello, World!. Line 4 is a comment.