When an appeal is worth writing
The strong case is factual error. A reviewer states your method does something it does not, criticises you for omitting an analysis that is in the supplementary material, or misreads a result. That is checkable, and an editor can act on it.
A second reasonable case is procedural: an obvious conflict of interest in the review, or a report so thin the decision cannot rest on it.
The weak case — and by far the most common — is disagreement about significance. If two reviewers judged the contribution insufficient and you believe they undervalued it, an appeal is unlikely to move the editor, who selected those reviewers precisely for that judgement.
Appeal a demonstrable error. Do not appeal a difference of opinion about how important your work is.
How to structure one
Read the journal's appeal policy first — most publishers have one, it states where to send the appeal and within what window, and appeals sent the wrong way are frequently not considered at all.
Then write briefly and without heat. Open by thanking the editor for the consideration, state plainly that you are appealing, and identify the specific factual points at issue. For each, quote the reviewer's statement and show the evidence that contradicts it — a line number, a figure, a passage in the supplement.
Close by saying what you are asking for: usually re-review by an additional reviewer, or reconsideration in light of the correction. Ask for something specific and achievable.
What to expect
Appeals take time — often weeks, sometimes longer, because the editor may need to consult the original reviewers or find a new one. During that period the paper is committed to that journal and you cannot submit it elsewhere.
That waiting cost is the real calculation. If the appeal is a long shot, the weeks spent may be worth more invested in reworking the paper for a better-matched journal. We would generally only advise appealing where there is a clear, documentable error.
One thing to keep in mind throughout: the editor is a colleague in your field who you will encounter again. An appeal written with restraint costs nothing. One written in anger is remembered.