Did armored cavalry have an advantage over unarmored cavalry in 18th/19th century?

The advantage of wearing cuirass was obviously protection. As you noted, it could deflect pistol shots, and in theory even muskets at distance. Perhaps the main benefit however, was in fact against other hors*m*n. Cavalry battles in this period often amounted to individual melee, and like the armour of old, the cuirass offered some defence against enemy sabres.

Of course, protection come at the cost encumbrance. On the battlefield it hinders the soldier's movements in a melee, and burdens the horse's speed, which was critical for the heavy cavalry charge in the age of firearms. Beyond combat concerns, the logistics of finding strong horses adequate for carrying the load was a significant practical and financial headache.

Thus, while the exact trade-offs between armour and flexibility may be a matter of debate, the cumbersomeness of the cuirass was a major complaint from contemporary cavalries. The Marquess of Anglesey, commander of British cavalry in the Peninsular War and later at Waterloo where he famously lost his leg, observed in a post-Waterloo memo that:

I think the Cuirass protects, but it also encumbers, and in a mêlée I am sure the Cuirass causes the loss of many a life.

_{Siborne, Herbert Taylor, ed. Waterloo Letters: A Selection from Original and Hitherto Unpublished Letters Bearing on the Operations of the 16th, 17th, and 18th June, 1815, by Officers who Served in the Campaign. Cassell, 1891.}

Likewise, Major North Ludlow Beamish, who served in the Dragoon Guards, noted in his translation of a Württemberg cavalry general's military treatise that:

Armour of any kind is highly objectionable for any cavalry . . . The enormous weight, - the constant clearing required, - the pain which its inflexibility must cause under fatigue, are circumstances which alone qualify its advantages in action . . . there can be no doubt that, however invulnerable a cuirass may render a cavalry soldier, his active properties are thereby much reduced.

_{von Bismark, Count. Vorlesungen über die Taktik der Reuterey. Bismark's Tactics and Manœuvres of Cavalry, translated from German by Major N. Ludlow Beamish, with notes by the translator. London, 1830}

Even Napoleon, who relied greatly on his cuirassiers as shock troops, lamented of them that:

One result of having men of large stature, is the necessity of large horses, which doubles the expense and does not render the same service.

_{Picard, Earnest. "Maxims and Opinions of Napoleon on the Use of Cavalry." Journal of the U.S. Cavalry Association 24:1002}

It should be noted that cuirassiers were by no means uncommon during the question's time period. Despite their drawbacks, most if not all the major armies of Europe maintained cuirassiers at some point in the 1700s and 1800s. Their popularity did wax and wane, however as late as 1872, an article in the United Services Magazine noted with some wonder that:

In spite of all these facts and reasoning, the cuirass is still retained in France, Russia, England and Prussia.

_{"The Future Tactics of Cavalry" United Services Magazine, vol 130, September 1872.}

The Austrians were a bit ahead of the curve here, having abandoned the cuirass in 1859. Previously however Austria alone of the major powers maintained cuirassiers through both the French Revolution and the Napoleonic Wars. Most other cavalries had entered the 1700s with cuirassiers, but abandoned them over the course of the century.

Napoleon's success in deploying cuirassiers as shock troops heralded a renaissance (or rather, a last hurrah) for the armoured heavy cavalry. The cuirass thus curiously re-emerged in several armies after Napoleon's defeat. Prussia, having abandoned the armour in 1790, re-equipped her cuirassiers with captured French cuirasses in 1814, as did the Spanish in 1810. The Russians likewise began equipping their heavy cavalry with personal armour in 1812.

Both Prussia and Russia had heavy cavalry that were styled 'cuirassiers', but this reflected tradition rather than equipment. Having abolished the Jurassic in 1790, Prussia only re-adopted it in 1814, while Russia only began to issue body armour in 1812 . . . Spain [formed] its single regiment in 1810, utiliziing cuirasses captured from the French 13e Cuirassiers.

_{Haythornthwaite, Philip. Napoleonic Heavy Cavalry & Dragoon Tactics. Bloomsbury Publishing, 2013.}

Even some minor powers such as Saxony, Warsaw and Westphalia raised some cuirassiers.

The British did actually have cuirassiers too, but they were not styled as such and never saw action wearing them. Three regiments of the Household Cavalry were equipped with steel armour after Waterloo: the 1st and 2nd Life Guards, and the Royal Horse Guards. The irony is observed by the aforementioned Major Beamish:

It is strange that armour should have been given to the British Life Guards immediately after they had proved its inefficiency, - after they, unaided by such defences, had torn the laurels of Waterloo from the cuirassiers of France.

_{von Bismark, Count. Vorlesungen über die Taktik der Reuterey. Bismark's Tactics and Manœuvres of Cavalry, translated from German by Major N. Ludlow Beamish, with notes by the translator. London, 1830}