In most appeals against conviction the focus is, to use the broadest of non-technical descriptions, on errors and on the soundness of the verdict at trial. In such appeals, differences among judges can occur on each of these matters.
An illustration is Hofer v The Queen  HCA 36 (10 November 2021).
On whether there had been a qualifying error, Kiefel CJ, Keane J, Gleeson J (jointly) and separately, Gordon J, held that there had been such an error. Gageler J, while agreeing with the plurality in dismissing the appeal, held that there had been no such qualifying error.
And on whether the verdict at trial had been sound, the plurality held that it was, but Gordon J held that it wasn’t, and Gageler J didn’t need to address this question.
The case is of wide interest to appellate buffs, partly because of Gageler J’s recognition that he was bound by an earlier decision of the High Court (Weiss v The Queen  HCA 81, discussed critically ten times on this site so far - use the search box) even if he disagreed with it, because its correctness was not in issue in this case: , and partly because of his discussion of how Weiss reorientated the function of appellate courts in deciding this type of conviction appeals: .
If appellate judges find that an error at trial was significant, in the sense that it created a real chance (etc, ) that it affected the verdict, then the appeal judges must themselves reach their own verdict on the available record (and on such new evidence as may be admissible on appeal), unless for reasons usually relating to the issues at trial - such as assessments of witness credibility - it is impossible to do so. The Supreme Court of New Zealand has given itself this function too, by means of what I think is a rather strained application of techniques of statutory interpretation. See my discussion here, on 1 July 2021.
The appellate verdict in Hofer was not unanimous. The majority verdict favoured the upholding of the conviction. As this verdict was not unanimous, should a retrial have been ordered? And, in any case where an appellate verdict unanimously favoured there being a reasonable doubt about the appellant's guilt, would it be appropriate to order a retrial, or should an acquittal be entered?
The plurality judgment in Hofer contains a helpful discussion of the implications of non-observance of the rule in Browne v Dunn in criminal cases: -.
 Update: For illustration of circumstances where the Court considered it was inappropriate for it to reach a verdict, and instead ordered a retrial, see Orreal v The Queen  HCA 44 (16 December 2021).