First, congratulations on receiving comments. Editors are often so overwhelmed with the number of submissions they receive that it's hard to find the time to comment. So they usually save that for the work they really want to encourage. Those comments are a good indication that your story made a strong impression.

Don't bother submitting a revision to the same journal. If an editor is interested in seeing a rewrite, she'll ask for it. (When that happens, by all means revise and resubmit.) Otherwise, you're better off sending a new piece to that journal. If you have something ready, follow up as soon as you can. Address the cover letter to the editor who wrote you the note and mention the title of the previous submission. You can acknowledge the editor's comments but don't go into great detail and don't get into an explanation (or rebuttal). This isn't an opportunity to rehash the past. Build off the positive response to the previous submission, but keep the focus on the new submission.

Do take another look at the story in light of the comments. Do you agree with the editor? If so, take those comments into consideration as you revise before sending the story out again. It will make your submission that much stronger.