By the time we get to Revelation 18:20, the beast-riding woman from chapter 17 is promised for swift destruction in a futile attempt at war against God.  And so we come to this: 

Rejoice over her, O heaven,
you saints and apostles and prophets!

But there is one more line to this.  The question is, what does it say?

KJV       for God hath avenged you on her.
NRS     For God has given judgment for you against her.
NET     (for God has pronounced judgment against her on your behalf!)
NIV      For God has judged her with the judgment she imposed on you.
HCSB  because God has executed your judgment on her!

These are NOT “the same in different words”; these are actually different.

1. The KJV brings in the notion of God’s vengeance/avenging, the rest speak instead of God’s krima, which has a range of meanings including final judgment or the concept of justice or possibly even lawsuit. It is true that 19:2 uses the word avenged/vindicated and is a kind of commentary on 18:20;  but the word in 18:20 is not vengeance. It rather has to do with a legal ruling and with justice—as if God has tried her in court and now has passed a legal ruling.  (This idea is common in Deuteronomy and various prophets.)
   
   
2. The NRS and NET do pretty much say the same thing as each other, just with different word order---although NET makes it all part of a parenthetical statement.
   
   
3. But the NIV is entirely different. Here the final decree is identified as the very thing the woman was doing against God’s people.
   
   
4. And the HCSB (Holman Christian Standard Bible) seems to make God’s people the judge!

What gives?

Well what gives is that the Greek text is difficult to understand.  This is not English translators “changing the Word of God!”  to suit their fancy.  This is English translators trying to figure out what the Greek text means so they can put it into English. 

The Greek text literally translated says this:
“because God judged the judgment of you from her”

Please don’t think we can figure this out from a so-called “literal translation,” because more is involved than just “fitting the words together.” Actually, the Greek clause is vague or even “awkward” (so says Koester’s commentary p. 708). Beale’s commentary (p. 917f) calls this “the most difficult in the book to translate,” and then he lists 5 alternatives chosen by different commentators!  The translation is complicated not only by the meaning of the word krima (judgment etc., see above), but also by two genitives:  the judgment of you, and also the words from her. (To illustrate, the former is not even clear for an English reader.  For example, does judgment of you mean your judgment against the woman or that the woman has judged you?) 

Although there are various legitimate possibilities (as noted above), all translation must take account of immediate context;  and the context of Apoc 18-19 is resoundingly clear in giving back (even a double portion! 18:6) to the prostitute Babylon for her atrocities against God’s faithful followers.  It is also worthwhile to spend some time in the NETS** translation looking up texts that use the verb and noun forms of the judgment words (krino and krima) in the same verse (1 Sam. 2:10; 1 Ki. 3:28; Odes 3:10; Job 31:13; Ps. Sol. 2:32; Zeph. 2:3; Zech. 7:9; 8:16; Isa. 16:5; Jer. 21:12; Rom. 2:3; 1 Cor. 11:29; Rev. 18:20). 

Since this is not a Greek discussion board, I’ll avoid the gritty details (yes, they get very detailed).  Just be aware that all of the translations above are possible and worth thinking about.  If you're teaching a class on this verse, you could even give all the possibilities along with the "so what" of each, and then move along.

These are only a fraction of the things translators wrestle with, and this is why there is no such thing as a perfect translation. It is valuable for English Bible readers to keep reading and comparing a variety of English translations.

(PS:  Now, in case you want to know:  although I’m not a huge fan of some things the NIV does, my own judgment for Rev 18:20 is that the NIV's approach here (which they did not create) is highly commendable.  In fact here is my translation of this text:

Rejoice over her,
O Heaven,
    O Saints,
          O Apostles,
               O Prophets!
Because God has judged her
     with her own judgment of you.

Gary D. Collier
IABC

**NETS = the New English Translation of the Septuagint, see link here,

***Luther's 1534 picture of the harlot on the beast has her wearing a papal tiara.