Hence, ou is objective.
              me is subjective.

              ou denies a matter of fact.
              me denies a matter of feeling.

              ou denies absolutely.
              me denies conditionally.

              ou negatives and affirmation.
              me negatives a supposition, and prohibits or forbids.

              ou is generally used with the Indicative Mood.
              me with the other moods of the verb.

For the difference, see John 3:18 :  "He that believeth on Him is not (ou) condemned :  but he that believeth not (me, supposing such a case) is condemned already, because he hath not (me) believed (according to the supposition made).  See also Matt. 22:29 :  "Ye do err, not knowing the Scriptures".  Had the negative here been "ou" it would imply the fact that they did not know, because of not possessing them.  But it is "me", implying the feeling; they did not wish to know. The same distinctions apply to all the compounds of ou and me respectively.

1. The two negatives when combined lose their distinctive meanings, and form the strongest and most emphatic asseveration; but, solemn and strong as it is, whenever it was used by a human being the result always belied it, and the speaker never made it good :--
   
   • Matt. 16:22.  Peter said, "This shall not be unto Thee".  (But it was)
   • Matt. 26:35.  Peter said, "I will not deny Thee".  (But he did)
   • John 11:56.  Some said, "What think ye, that He will not come to the feast?"  (But He did)
   • John 13:8.  Peter said, "Thou shalt never wash my feet".  (But He did)
   • John 20:25.  Thomas said, "Except I shall see ... I will not believe".  (But he did)
   
   
2. On the other hand, when the Lord used this solemn asservation it was always absolutely true, and was, or will yet be made good.  It is variously rendered, as a simple negative (as above); no, not, by no means, in no wise, or in no case, &c.
   
   This expression was used by our Lord on forty-six separate occasions (omitting the parallel passages, which are placed within brackets), adding three (Matt. 25:9.  Luke 8:17, and John 16:7), and omitting two (Matt. 24:2 and Luke 22:34), with the critical texts.  They are as follows, and are all worthy of the closest attention (see Matt. 5:18; 16:28; 24:34.  John 6:37; &c.).
   
   Matt. 5:18, 20, 26; 10:23, 42; 13:14; 15:6; 16:28 (Mark 9:1;  Luke 9:27); 18:3 (Luke 18:17); 23:39; 24:2  (omitted by all, but retained in Mark 13:2), 21, 34 (Mark 13:30.  Luke 21:32), 35 (Mark 13:31.  Luke  21:3 422 3); 25:9 (added by all); 26:29 (Mark 14:25.  Luke 22:18).
   Mark 9:41; 13:2 (omitted in Matt. 24:2, retained here); 16:18.
   Luke 6:37; 8:-17 (added by most); 10:19; 12:59; 13:35; 18:7, 30; 21:18; 22:16, 34 (omitted by all,  retained in John 13:38), 67, 68.
   John 4:14, 48; 6:35, 37; 8:12, 51, 52; 10:5, 28; 11:28; 13:38 (omitted in Luke 22:34, but retained here); 16:7 (added by some).
   
   
3. The expression ou me is used once by an angel (Luke 1:15).
   
   
4. Fourteen times by Paul :  three in Acts (13:41; 28:26), and eleven times in his Epistles (Rom. 4:8.  1Cor. 8:13.  Gal. 4:30; 5:16.  1Thess. 4:15; 5:3.  Heb. 8:11, 12; 10:17; 13:5).
   
   
5. Twice by Peter (1Pet. 2:6.  2Pet. 1:10).
   
   
6. Sixteen times in the Apocalypse (one being added in all the critical texts, 9:6) :  Rev. 2:11; 3:3, 5, 12;  9:6; 15:4; 18:7, 14, 21, 22, 23; 21:25, 27.