I think the biggest changes if Bourgogne survives is the fact his eldest son doesn't die, OTL Louis "after me, the deluge" XV never rules (nor is there a rush to marry him to the daughter of the former king of Poland) and probably has a very different character, and there are probably more children to come. No possible succession crisis, no Regency (and the Orleans family is farther and farther from the throne), Bourgogne was a very priggish devout Catholic (monkish before he was married) and so the frivolity of Louis XV's court doesn't happen. His brother, the Duc de Berri (who was cut from the same cloth as his easy-going father, the Grand Dauphin) probably has his death butterflied since its easy to imagine he wasn't in a hunting incident as in OTL. Bourgogne was also VERY close to his brother, Phillip V of Spain (one biographer said his brother Louis's death was the greatest blow of Philips's life) and their wives were sisters. The alliance between France and Spain would be airtight as long as both rule. And although Bourgogne was known to be a priggish Catholic, he was also before his death widely popular with much of the masses as they saw in him change from his grandfather.
The two wild-cards:
The Duke of Brittany who, surviving, becomes in TTL Louis XVI. What to make of his character? Who does he marry? With both parents alive he probably turns out very different than his brother, OTL Louis XV.
Marie-Adelaide. One of the most interesting personalities of the era. One of only two women Louis XIV was said to ever truly love (the other being his mother). She pretty much had the entire court - including her husband, her brothers-in-law, the Sun King, Madame Maintenon - wrapped around her finger. By all accounts she was a loveable scamp who got away with everything. Even her step-grandmother (the Duchess of Orleans, Liseleotte) was fond of her and she usually didn't like anyone at the French court. She was clearly devoted to her husband's prestige (and to him, after she became Dauphine) as she engineered the downfall of the Duc de Vendome. Her sister, the Queen of Spain, was also of a similar character. I would even wonder if Philip V marries the Parma heiress if Marie-Adelaide is still alive and has a say in it. Marie-Adelaide and Bourgogne were also close to James, the Old Pretender and to Louisa Maria (the Princess over the Water) who were in their little group. I would say there might be a greater assistance from France in 1715 to James or in 1745 to the Bonnie Prince.