I have worked for both of the companies you mention, hoping to get involved with the interesting technical problems they are famous for, and in each case I was

I have worked for both of the companies you mention, hoping to get involved with the interesting technical problems they are famous for, and in each case I was disappointed. What I observed was that you cannot really get a job doing the interesting work, not directly, because a megacorp does not hire for those positions; those core jobs go to trusted veteran insiders. The organization grows from its edge, not its center; as a newbie, you will most likely be assigned to some minor piece of functionality extending the outlying periphery of whatever it was you actually wanted to work on. If you can stomach that for however many years it takes to build up an internal reputation, you may eventually be able to move inward toward the job you actually wanted; but there is no guarantee this will be possible.