I am going to throw this out there as someone who served in Japan, which I consider to be one of the more difficult languages out there, but I think that the language abilities that a missionary gains on his/her mission really depend on the effort they put forth. The following is obviously anecdotal data (and it's long - sorry!), but I think that a mission can be 100x more effective for learning a language than college if you like learning things at a pace and in a manner that matches you instead of conforming to a teacher or curriculum. Here is my "success story" with the Japanese language and what I think missionaries need to do to become "fluent" (because it's too late to become "native"):

Although a lot of the missionaries I served with in Japan wasted their time studying the gospel in English, I spent most of my time studying the language; for example, I read the Book of Mormon in Japanese from front to back several times within my first year there. By that time, I had also gone through multiple books on Japanese grammar that I picked up from a local bookstore. I then went out and bought Japanese history books and read them during my morning study instead of the reading the scriptures. After a year in the field, the mission president started to ask me to do simultaneous translation for the Japanese missionaries during zone conferences or other special occasions, like when when apostles and other English-speaking LDS celebrities would visit the mission. (Looking back on it, I wasn't very proficient at the time, but that practice was better than anything you do in college because it was real interpretation and not a fake scenario.) I would keep in touch with the Japanese friends I made and companions I served with via after I transferred away. I made a slot on my bicycle where I could put index cards so that I could remember sentences and vocabulary I read in the books I had purchased. I kept a small notebook in my pocket and carried an electronic dictionary, and would write down every new word I heard.

After I got back from my mission, I went to a non-BYU elite private university. I easily tested out of all of the undergrad language classes, so they put me in language classes with the graduate students; even those proved to be easy (I managed a 4.0 GPA without ever really trying). Within several months of coming back from my mission, I took and passed the highest level (N1) of the Japanese Language Proficiency Test, which even college graduates who major in Japanese generally have trouble passing. I then went back to Japan to study abroad after my sophomore year, and during my junior year, I passed the Level 2 of the Japan Kanji Aptitude Test, which less than 25% of native Japanese high-school graduates pass, with nearly a perfect score. I also supported myself during my time abroad by winning international speech contests that had grand prizes in the thousands of dollars, and most of the other contestants were Chinese and Koreans who had been living in the Japan since they were little. I've since done simultaneous interpretation for the management of Global 500 companies as well as drafted everything from technical specification sheets to legal documents in Japanese.

Anyway, I just wanted to throw this out there because I actually really enjoyed my mission and I don't think I would have learned the language as well if I had tried to do it solely in a classroom. I think that missionaries hurt themselves by following rules like "you're not allowed to read newspapers"; "you can't buy non-church books"; "you can't communication with anyone from the areas you transferred out of"; etc. because you cannot expand your vocabulary and cultural understanding without reading, watching, and hearing the stuff that natives do. If a missionary follows all of the rules, then yes, he/she probably won't be very proficient. However, if he/she takes advantage of the 2 years he/she has in that country, it can be a great experience and he/she can come home in a much better position than someone who has studied the language for 2 years at college.