On his wonderful blog, Dr Michael Liccione was having a discussion with a Protestant systematic theology professor on this very subject. The Protestant professor succinctly explained the difference between the two understandings of Scripture (highlights by me):
The difference here is between a blueprint to make a building, and the bricks of which the building is made. A merely materially sufficient Scripture is like a pile of bricks that can build anything from a cathedral to a tool shed, but the bricks themselves possess no inherent intelligibility (formal sufficiency) in one direction for another. The intelligibility derives from outside the bricks. Conversely, a blueprint is inherently intelligible, and thus has not material but formal sufficiency to create a specific building, whether cathedral or tool shed.The distinction here makes all the difference in the world. From a Protestant point of view, anything less than formal sufficiency is unacceptable and will render Sola Scriptura impossible. On the flip side, the Catholic has no problem affirming the material sufficiency of Scripture (i.e. all necessary information is at least implicit in Scripture), since it in no way rules out the need for a Magisterium - and indeed demands one!
In terms of development, the claim that Scripture is materially sufficient presumes that the intelligibility of revelation derives from elsewhere than Scripture itself. A definitive magisterium (or external tradition) is necessary to decide what to do with the bricks. Without the magisterium it is impossible to know whether the bricks were intended to be a cathedral or a tool shed.
This is important to keep in mind because it makes the Protestant task of proving Sola Scriptura from the Bible more difficult and uncomfortable. It is not enough for the Protestant to point to a text that says how good or useful or inspired Scripture is, since the material sufficiency gladly embraces all this. The Protestant must show that Scripture formally and clearly lays out Christian teaching in such a way that no Magisterium or Tradition is needed, and in fact must show that the Magisterium and Tradition dont exist in the first place (or wont exist at some future date).
What is also important to point out is that the great majority of Scripture is not written down in any "blueprint" sense such that the Inspired human writer was laying down a systematic treatment of doctrines. In other words, the Bible is not written like a text book or even a 'do it yourself' self-help book. This is a major difficulty for the Protestant seeking to prove formal sufficiency.
Take the example of Baptism: If Scripture were formally sufficient, it would have to lay out in a very systematic manner what effects Baptism has on the individual, whether it is required, who can be Baptized, and how to Baptize. Contrary to the formal approach, what happens in real life and throughout history is that theologians of both the Protestant and Catholic camps have had to "derive" various doctrines like Baptism piece by piece, starting with the explicit references to baptism, then any allusions to it, and then the support of related doctrines, all to come to their final conclusions on Baptism. As everyone is aware, there is no such systematic treatment of Scripture on this teaching - and as everyone is equally aware, Protestants have disagreements on every one of those facets mentioned (e.g. whether infants can be baptized).
Given this very solid example against the notion of formal sufficiency, we can have great confidence that no specific passage will ever teach formal sufficiency (since the Scriptures cannot contradict or mislead).
Probably the most famous - and most important - example that contradicts formal sufficiency is all the heresy surrounding the Trinity. As Catholic Apologist Dave Armstrong explains: "The [Trinity] can be proven from Scripture, indeed (material sufficiency), but Scripture Alone as a principle was not formally sufficient to prevent the Arian crisis from occurring. In other words, the decisive factor in these controversies was the appeal to apostolic succession and Tradition, which showed that the Church had always been trinitarian."
Other examples (among many) that contradict the notion of formal sufficiency are especially those texts discussing interpretation of OT prophecy, which the NT shows was very often missed by the Jews who knew the OT quite well. The Road to Emmaus (Lk 24:13-27), the Bereans (Acts 17:1-5,10-12), and Apollos (Acts 18:24-26) demonstrate the problem quite well.
One last important thing to note (as apologists like Mark Shea and Dave Armstrong point out) is that when one affirms the material sufficiency of Scripture, there is no "fear" of "undermining" the authority of Scripture or "subordinating" the authority of Scripture with Tradition or Magisterium - fears which Protestants regularly inject in such discussions. The reason why there is no such "fear" from the Catholic end is because material sufficiency by *nature* means Tradition and Magisterium are necessary to arrange the "bricks" in the right order to form the right structure. That "fear" can only exist if the Protestant can demonstrate formal sufficiency to be true - and until then is fallaciously fear mongering.