Most of the time, Louis XVIII's success is explained by the fact that he was concilient while Charles X 's failure is explained by the fact that he was intransigent.
It is actually more complicated.
In 1814 and 1815, France was defeated, had lost many soldiers and much money. It was a country that needed to recover.
In 1830, France had recovered. Liberals considered that they did not need the Bourbons anymore and that it was time to pursue the French Revolution. At the same time, there was a new generation of young people in their twenties who were still children in the Napoleonic times. These young people saw essentially Napoleon's military glory without actually realizing the price to pay (fights and death of innocent people). As a result, they despised the Bourbons. Without this generation, it is likely that the Revolution of July would never have occured.
It is true that Charles X was more absolutist than Louis XVIII (at least after they came back to France: Louis XVIII was very absolutist too in exile). Before becoming king, he criticized Louis XVIII and his Charter very much. However, when he became king himself, he accepted said Charter and respected it. He probably realized how much it would've been dangerous to refuse it. Before dissolving the Chamber in 1830 (which the Charter authorized), he hesitated very much because he knew it was a risked move. He decided to take the risk. It was a mistake.
Considering all ot that, I think it is highly likely that an agreement would've been found in 1814, just as in OTL, even with Charles X instead of Louis XVIII. Then, the Hundred Days would've likely followed the OTL path too.
Things become more complicated after that.
Here, I see two options:
1. Charles X comes back to the throne.
2. The Allies are not confident enough in him and refuse to let him come back.
If Charles X comes back, he is unlikely to dissolve the Chambre Introuvable as Louis XVIII did. There, either the liberals win and there is a new revolution in 1815, either the royalists win and the Restoration becomes more absolutist than in OTL.
If Charles X can't come back, I agree with dcontreras. There are good chances that his son Louis-Antoine would've become king instead of him.
(However, he would've still been numbered Louis XIX and not Louis XVIII as Louis-Stanislas would've still been numbered Louis XVIII just like Louis-Charles was numbered Louis XVII. Except of course if the POD is that Louis-Stanislas dies even before Louis-Charles.)
Louis-Antoine becoming king before his father's death may have been presented as a legitimate move. After all, at the beginning of the Capetian dynasty, the king's eldest son was crowned and held the title of king before his father's death. Louis VII even had passed effective power to Philippe-Auguste before dying.
I guess it is hard to figure what Louis XIX's reign may have looked like. Louis-Antoine is known to be the least absolutist of the immediate family but he was far from being like Louis-Philippe. The Charter was perfect in his eyes. I guess liberals would've still seen him as too absolutist. He may have been more prudent than his father though.
That would include Louis Philippe who was 4th in line of succession after Charles and his two sons when Louis XVIII was restored, and after Charles X's abdication, he was third in line of succession behind Angouleme and his nephew the young Henri (Before he usurped the young Chambord whom Charles had left in his charge.).
The succession line was not that clear. No official document of the Restoration precised it and it was likely on purpose.
Louis XVIII wanted the Bourbon-Anjou to be the successors if the eldest branch went extinct. Charles X, on the opposite, favored the Orléans.
(I know: it is surprising. The opposite may have been more expected.)