Cut barrels are superior in a number of areas. For one thing, the rates of twist are considerably more accurate. Ramming the button through different areas of homogeneity in the steel results in inconsistent rates of twist as the button can "drag" rather than rifle.
The big issue is the stress. Displacing the steel to create rifling stresses the steel a great deal, and while good-quality button barrels undergo a process of stress-relieving, it does not completely remove all stress. Because the bore of a button-rifled barrel "springs-back", the bore is typically uneven and requires extensive lapping, and the lapping required in itself can be detrimental. A barrel with latent stresses will change dimensionally to a marked degree when heated. Buttoned barrels should never be fluted because of the latent stresses and fluting is a mechanical form of stress relieving.
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I know Mick McPhee is highly critical of one buttoned barrel maker, due to the markedly uneven bores he has come across as a result of short-lapping.
Having said all that, there are some very good button rifled barrels out there, and Dennis is right, that a number of BR records have been set with them but I highly doubt many of these records were being set with barrels that had 2500 rounds down the pipe.
One of the best BR shooters in the world - Lester Bruno - is a cut rifled barrel fanatic. I would also say - anecdotally - that F-Class tends to be dominated by cut rifled barrels, where the choice of cartridges prefers longer barrels.