I also think there will be a great ideological struggle in the decades to come, but I don't think it will be among the world's religions to see which one comes out "on top." Religions are highly hereditary, and as such are highly stable geographically. For instance, India will likely remain predominantly Hindu, the middle East predominantly Muslim, the West predominantly xtian, etc.
No, the struggle I see ahead--arguably, it's already happening today--is between religion in general and rational thought. More and more, society seems to be getting divided not along class lines but between the intellectual haves and have-nots. On one side you have a fairly scientifically-literate population which is slowly coming to reject superstitions and unfounded beliefs in all their forms, including as religion. This is exemplified by such groups as the scientific community, the so-called "new atheists," and many working in the information sector (engineers, I.T. people, etc.) On the other side are those who embrace belief as a strong part of their lifestyle, the anti-intellectuals who see science and rational thought as a trend toward a more hedonistic, politically-liberal society that is a threat to their core beliefs and vision of how society should be. This side includes groups such as evangelicals, creationists, ultra-nationalists, and strong political conservatives. They see science and rational thought not as tools for acquiring knowledge, but as a belief system in competition to their own.
This struggle is happening on many fronts: in the schools, in politics, with civil rights. We can see this struggle in the repeated efforts to get creationism mythology taught in the classrooms, gov't funding of particular scientific endeavors like stem cell research or cloning, the countless legal battles (which rarely make headlines anymore for some reason) to keep church and state separated, the rise in popularity of both evangelicalism and science/atheism movements, and the endless back-and-forth dialogue between evolutionists and creationists.
Which side comes out ahead in the end will determine the future of our society, and I think both sides realize this at some level and recognize the importance of promoting their side. I am, of course, rooting for a more rational, scientifically-literate society where no religion is favored by gov't and policy decisions are evidence-based rather than belief-based or dogma-based. Such an outcome will minimize societal strife while maximizing both cultural diversity and economic prosperity.