The granting by the legislature of unfettered powers on a court does not destroy all lawful restraint. In Lacey v Attorney-General of Queensland  HCA 10 (7 April 2011) the High Court considered statutory interpretation, legislative purpose, jurisdiction, power, and the kinds of appeals that can exist.
The majority, French CJ, Gummow,Hayne, Crennan, Kiefel and Bell JJ, held that a provision saying an appellate court "may in its unfettered discretion vary the sentence and impose such sentence as to the Court seems proper" means that the appellate court must first be able to identify an error in the decision of the court below, and then the "unfettered discretion" gives the appellate court the power to do what it considers the lower court should have done .
The principle of legality is "the presumption that, in the absence of unmistakable and unambiguous language, the legislature has not intended to interfere with basic rights, freedoms or immunities" , and "judicial findings as to legislative intention are an expression of the constitutional relationship between the arms of government with respect to the making, interpretation and application of laws" [ibid].
The distinction between a power and the jurisdiction to exercise it is such that "The power given to the Court may inform the characterisation of its jurisdiction but does not necessarily define its content" .
Here the jurisdiction was indicated by the heading to the relevant provision, here simply the word "appeal". This encompasses the jurisdiction, and the question is, what kind of jurisdiction does it create? .
The majority set out the relevant classes of appeal for present purposes  (footnotes omitted):
Heydon J dissented, holding that the appellate court had first to decide whether it disagreed with the sentence imposed by the lower court to the extent that interference was merited, and if it did, then to vary the sentence in accordance with its perception of what was appropriate .
So the difference here was in practical terms about which sort of appeal was created by the legislation, and this difference was reflected in different use of legislative materials (here, speeches in Parliament). The majority noted  (footnote omitted):
"The Minister's words ... cannot be substituted for the text of the law, particularly where the Minister's intention, not expressed in the law, affects the liberty of the subject. In any event the Minister's Speech left open the question of the content to be given to the word "appeal" and thereby to the jurisdiction conferred upon the Court."
The last thing I want to do is to reveal my unsubtle mind, but I must be frank and admit I find the distinction between the first and third classes of appeal as described by the majority rather elusive, apart from the possible add-ons in the third. This, I trust, is the judges' fault, not mine. More clarity in future please.