I don't think it's so much that the Jacobites had the best tunes, but that they get the same kind of romanticised image remake that the English Civil War Royalists and the Confederacy sometimes get.
As in they were noble, romantic, inspiring but quite wrong, as contrasted to their opponents who were dull, boring, serious and generally speaking right. Which completely ignores the issues involved and history of course.
Back in the 1960s the BBC broadcast an annual series of radio programmes aimed at junior schools called 'Singing Together'. It not only got kids singing but also presented (often bowdlerised or re-worked by 'real' arrangers) versions of a lot of folk songs from all over the world. I remember my entire class belting out 'Bonnie Dundee' without the slightest clue who this 'Dundee' person was or what he did.
Obviously, going from the lyrics, he was some kind of military hero and equally obviously Scots.
It was years later I discovered the lyrics were written by Sir Walter Scott (the same Scott who pretty much created the idea of clan tartans and highland dress) nearly 150 years after the event. Which was the 1689 Jacobite rising in which the Laird of Claverhouse, known as 'Bonnie Dundee' played a leading role and died during the Jacobite victory of Killiecrankie. Far from being a nice romantic hero, before the uprising Dundee had been in the lead of persecuting Scots Covenantors who amongst other things opposed the revived Stuart monarchy and wished to retain parliamentary government rather than have a king ruling by absolute 'divine right'.
Still, the song has a great tune, which like many used for Jacobite songs was around a long time before there were Jacobites.
The anti-Jacobites did have songs and tunes, but being the government side tended to have them written or at least poshed up by composers and arranged for 'proper' bands to play. So they're mostly very 'standard issue 18th century military music', the most famous being the British national anthem though these days we generally miss out the verse about sending an army to crush the rebellious Scots.