This thread has relevance primarily to the courts of the common law tradition. Adversarialness plays a different and diminished role in civil law regimes, e.g. in Europe.
That so much of the discussion has been about criminal law invites some amplification. Even in common law jurisdictions, the criminal process is adversarial in a modified respect as compared to the process in contract, tort, or the other areas of the civil courts (not to be confused with courts of the civil law system).
The defense counsel in a criminal case is very nearly an unlimited advocate. He may, and often should, try to bring the jury to believe the opposite of what he knows to be the truth. There are some limitations. He cannot ethically put in evidence he knows to be fraudulent or induce, encourage, or abet witnesses in giving testimony he knows to be false. It is, however, ethically permissible to make a prosecution witness that he knows to be telling the truth seem, in the eyes of the jury, to be an abject liar.
Prosecutors are advocates bound by some important restrictions. New prosecutors are always told that their job is not to get convictions, but to do justice. Any experienced prosecutor will have dismissed cases when she found that the evidence didn’t support conviction.
A prosecutor must have a higher degree of confidence in the truthfulness of a witness than would a defense counsel before putting the witness on the stand. An ethical prosecutor does not make a defense witness appear to be lying if the prosecutor believes that the witness in fact is telling the truth. (The prosecutor’s time line would be easier if the jury didn’t believe the witness that the defendant got to the party by 9 pm, but the witness is probably telling the truth, and the prosecutor will just have to show that it is possible to get across town in the time that leaves.)
It is still an adversarial process, but a modified and asymmetrical one. In a contract case, it is symmetrical.
Most participants are less pessimistic than the general public about the right people getting convicted and the right ones acquitted in the criminal trial system. Even those juries that seem to reach their verdict by an odd route usually arrive at the right destination. It happens that utterly innocent people are convicted by juries, but it does not happen statistically often. It happens a little more often that guilty people are acquitted, but this is something we should expect with the higher burden of proof on the prosecution (and the prosecution’s more stringent ethical constraints). It is the outlier cases that are newsworthy, and that we remember, as in the tragedy of the prisoner found innocent by DNA evidence after a couple of decades of incarceration.
The same level of confidence is not shared by participants in convictions by plea bargaining, which is to say the great majority of convictions. Still most of those convicted are guilty, at least of something, but the incentives for the innocent to plead guilty are often very great.
The very poor are usually defended by very competent, if always overworked, public defenders. (It is those not quite poor enough to qualify for a public defender who have the weakest representation in many parts of the United States.)
More important than the courtroom prowess of the well paid defense counsel is the time and resources she has for out of court investigation. When the defense seems to have a better command of the facts than the prosecution, the prosecution is in trouble.
In civil cases a disparity in wealth tends to make a far greater difference than it does in criminal cases. The poor can rarely expect to come out well in a contract case against a big company.
The justice of system of justice is a large and difficult question theoretically, politically, and practically. The justice of the adversary system is simpler if not simple. For a criminal trial, the thing of greatest concern is that the innocent are not convicted. This the common law countries do pretty well. Whether the inquisitorial system on the Continent does better, is an empirical question, though one methodologically challenging.
When what is at issue is plea bargain rather than trial, the adversarial nature of the proceeding is very much less, and the risk of innocent conviction is much greater. If you have any interest in the distantly related question whether plea bargaining is constitutional in the United States, you might look up my blog in a couple of days.
http://www.LawrenceCrocker.blogspot.com. There are a couple of preparatory posts there already on the constitutionality of trial by combat and of bench trials.
In civil cases the adversarial system usually favors wealth.