It's quite a bit more complicated than that. In a nutshell: there are the FACTS in a case; there is the LAW that governs the case (either prior cases or laws passed by a legislature); there is the LAWYER who represents a client, there is the JUDGE who applies the LAW to the FACTS, and sometimes a JURY that determines which FACTS are true.
A skilled lawyer can be better at: 1) uncovering the FACTS of the case (through the expert use of discovery techniques and motion practice); 2) explaining to the JUDGE how the LAW, or in some cases which LAW, should be applied to the FACTS; 3) arguing and presenting the CLIENT's case to the JUDGE and JURY.
None of this means, of course, that EVERYONE is entitled to a highly-skilled lawyer. As Clement said yesterday during oral argument, "you get what you pay for." Having said that, if your lawyer commits outright malpractice, you have a remedy against her.
I think that the Chief Justice was playing when he suggested that it's the JUDGE and not the LAWYER who is responsible for getting things right--he knows well the benefits of high-quality lawyering.
And I think Justice Scalia was off base when he suggested that JUDGEs don't tell LAWYERs about the quality of their performance. They do it all the time--both when the quality is good and when the quality is poor.