I believe the ideology of imperialism is stronger and is more likely to win when opposed to jihadism. Jihadism is a sect or small group, while many countries in the world support imperialism. Suggesting that jihadism could potentially over rule imperialism seems a bit silly to me. Jihadism comes from an extremist view that few can connect with.
While it is arguably the lesser of two evils, Imperialism will certainly take the place of Jihadism. National ideologies and armies/economies are simply too powerful to crumble under the weight of ragtag terrorist forces in the Middle East. If, eventually, imperialist forces reach a peak at which the US or UN decide to simply conquer or take over Islamist countries, they certainly have the power and armaments available to do so.
I think that imperialism will win over jihadism, because jihadism cannot control everyone all over the world. With imperialism, people might not be allowed to be in charge, but they generally are allowed to go about their business and live moderate lives. Jihadists cannot possibly control everyone in the world at once.
As it stands right now, I think that imperialism will win out over jihadism because jihadism is primarily a religious fanatical group bent on distruction. Imperialism, which has a lot of problems too, is practiced by people with power and money. Imperialism will more than likely win our over jihadism.