ICR is a prestigious institution, and is very well-regarded by scholars in the U.S. (and apparently internationally, as well, since you said that ICR is well known in South Korea). The ICR (and UIUC in general) is definitely a top-tier program, consistently ranked as one of the best communication programs in the country. Pittsburgh does not have the same level of reputation, and is at best a "second-tier" (and honestly probably a "third tier") program. You can compare the programs in different rankings to get a sense of their different standings; I wouldn't make a decision based solely on rankings, but they can be useful just to get a sense of the programs' reputations among scholars in the discipline.
It sounds like a faculty member at Pitt is doing research in your area of interest, and really wants to work with you to further their own research agenda. This may also explain the more generous financial offer from Pittsburgh (which is surprising considering the disparate resources between Pitt and ICR). These are both exciting opportunities to consider! If I were in your position, I would think about what I want to do after finishing the PhD. Do you plan to stay in the U.S., or will you return to South Korea? For example, if you plan to work in South Korea after earning your PhD, it could be very helpful to have earned your degree from an institution that is well known and has a good reputation. So in that sense, getting your PhD from ICR could benefit your job search because it is known in South Korea (it would also help if you stayed in the states, as ICR is such a prestigious program, but that doesn't mean that doing your doctorate at Pitt will hurt you). Whatever you choose, congratulations! It is a good dilemma to have! I did not get accepted to ICR, and it would be wonderful to attend that program!