In cases that went to trial they did equally well, but private attorneys fared better during plea negotiations. It isn't clear if this was due to the nature of the cases (with the marginal good cases seeking private counsel) or if this was due to better lawyering.
A counterpoint to this is a recent study on attorney effectiveness in tax court, which compared settlement and trial outcomes in pro se cases to those in lawyered cases.
Interestingly, the study found that the presence of an attorney for the taxpayer significantly improved the taxpayer’s financial outcome in tried cases, an effect that increased with the experience of the attorney. No such effect existed in settled cases. Although the latter result initially is surprising, it highlights the paramount importance of procedural expertise in formal trial proceedings, as opposed to negotiations with the opposing party. The study also found that the presence of an attorney for the taxpayer did not affect time elapsed to trial or settlement. Thus, the study found that taxpayers’ attorneys, who generally are paid by the hour, neither prolonged disputes nor expedited their resolution but did significantly improve the financial outcomes of the cases they tried.
Thus, in tax, lawyers help at trial, but not in the civil equivalent of a plea bargain. This may indicate that having no lawyer at all, as opposed to a different kind of lawyer does matter at trial, and that the I.R.S. is considerably better at enforcing low level uniformity and discipline on its trial lawyers than most district attorneys' offices.