Well as far as the USA the groups have always been more Christians, think about it
Filipinos - Huge Catholic Communities due to the Spanish conversions
Koreans - pretty much the only area evangelicals/protestants ever had real successes with. Most Koreans who come here are Christians already
As for other groups - I visited a Chinese Evangelical Church a couple of times....and they are VERY into converting as much of China as possible. Even in the church They had a power point presentations which included slides of populations growth (scaring the people by talking about how many Muslims lived in China and showing pics) of each religion broken down through statistics, etc. They talk about what they have done (and they pour a TON of money trying to convert people)
Personally I was a little disgusted with the whole concept of "harvesting souls"....the friends I went with thought that every Church was always so goal oriented about converting other people and suprised that I've never encountered that no matter what Mosque I went to.
I also think there is simply the element of being Western and influencing the people and how they think.
But in terms of the other religions...Judaism doesn't actively seek converts - Islam does, but not in the ultra proactive method that Christianity uses (its more like ask me and I'll talk...rather than find you) - Buddhism will have "missionaries" but they do things through example to show how they live rather than again, be so proactive (again notice how the Christian groups that are sky rocketing are the ones looking for many "souls to harvest" - hence its the evangelicals who are really growing)...I have no idea how Hinduism does it - but I'll assume it isn't great if its focused largely in the Indian Subcontinent (Although I have seen plenty of guys at my campus do advertising and hand out copies of the Bhagavid Gita (spelling?) which does a good job of getting the essence of hindiusm compared to the other thousands of texts they have (or so I'm told by some Hindus

)