One of the rallying points of Protestants against the orthodox Catholic hierarchy was the latter's emphasis on clericalism. To varying degrees, during that period, the orders you mentioned had strong history of clericalism, what with their emphasis on monastic order and monastic life.

In contrast, the Jesuits did away with community-centric decision-making, many of the monastic worship, and even regulation on distinctive dress. They were encouraged to go forth and engage with the populace as much as possible, and stressed personal initiative within a looser hierarchy. Loyola fought very hard against tendencies toward elaborate ceremony or ritual. He also emphasized communion and confession above other sacraments.

Later on, as Counter-Reformation became more emphasized, the Jesuits focused on two fronts: aggressive confrontation against northern European Protestantism and education. Neither of the two was novel, so there was quite a bit of resentment from the older orders toward the Jesuits.

Over time, Jesuit investment in university education paid off as nobles educated in these universities unsurprisingly chose Catholicism, and these tended to be sternly Catholic. William Lamormaini, SJ, confessor to HRE Emperor Ferdinand II, confidently stated, "'if there had been no schools of the Society founded by the prudent design of the emperors and archdukes in Vienna, Prague, Graz, Olomouc and elsewhere in Germany, there would have remained scarcely a vestige of the Catholic religion." Such was the influence of the Jesuits among the Habsburg lords. Jesuit monks and priests were also common features of Imperial armies.

So the success of the Jesuits were due to two factors: First is their engagement and efficiency; Second is their political influence among the Habsburgs.