Basic Constitutional rights tend to err in favor of the Defendant. Specifically, when the founding fathers inked the constitution, they did so with the understanding that the government was not to be trusted. This distrust of government naturally leads to the conclusion that it is better to allow a guilty person free than to punish the innocent. Thus, the "beyond a reasonable doubt" burden of proof in criminal cases.
As to the issue of appeals, notions of "due process" require that defendants be given a full and fair opportunity to offer a defense. I think most people agree that erring on the side of allowing someone to fully present a defense is better than erring on the side of a presumption of guilt. However, the due process requirements which allow the Court to reopen the case when new evidence is discovered is not unchecked. To reopen the matter for hearing, the defendant must show not only that the new evidence was not reasonably discoverable during the course of discovery for the initial hearing, but they must also show that the newly discovered evidence has a substantial likelihood to alter the outcome of the case.
Not really sure there's a better system...
-Mr. Spatts