In what I write next, I am speaking only for Canada, but there's really not that much difference between us and the U.S.
Appeal Court judges have the authority to uphold, reverse, or modify the trial decision. The appeal judge may also order a new trial. However, an appeal judge is required to show deference to the trial decision, and cannot allow an appeal simply because he or she views the evidence differently than the lower court did.
Thus, an Appeal Court would not overturn a jury decision merely because they think the jury should have voted other than they did. And if the Appeal Court finds that the judge erred in instructing the jury, or in some other way, it would routinely order a new trial -- again by jury. Sometimes appeal courts find that the judge erred in sentencing, and may modify the sentence without touching on the finding of guilt by the jury.
