Source: Judith Hauptman's "Mishnah As a Response to 'Tosefta,'" which is in Specific Problems in Rabbinic Literature.
According to Hauptman, the Mishnah is a reworking or a supplement of an earlier Tosefta. Hauptman argues that the Mishnah is an opaque source compared to the Tosefta, which elaborates on issues a lot more. One can understand why someone would write the Tosefta after the Mishnah--to clarify the Mishnah's ambiguities and to elaborate on what the Mishnah says. But why would anyone compose an opaque source, when a clear source already exists?
Hauptman states the following in response:
"The answer is that the clear source is still 'there,' available to the reader. The opaque source functions like an addendum to the clear source for the purpose of presenting a different view of the halakhah. The ancient reader would read the two together, just as the early layer of the gemara would read a mishnah together with related beraitot" (33).
Hauptman points out examples of the Mishnah differing from the Tosefta. But I wonder if her thesis accounts for everything. What about when the two agree? Why would the Mishnah regurgitate and condense what the Tosefta says? I'm not saying it's impossible, but the question deserves an answer. And why can't we say that the Tosefta disagrees with the Mishnah when there are differences?