Well, I can already see I'm going to be outnumbered on this, but in any case, since nobody else seems to be willing to say even a word in their defense against all the calumnies that are uttered against them here, let me just say that the FSSP does for the last 25 odd years merely what the SSPX and other traditional groups did for about 20 odd years before that - to form orthodox priests in Catholic seminaries, such as are most badly needed today, with solid doctrinal catechesis and traditional liturgical orthopraxis, and all this under the legitimate Roman authorities, again, like the SSPX always did from the beginning, and who still recognize that authority.
It's amusing that the primary reason offered by most of the people in this thread is a reason declared avowedly false by all the SSPX theologians, the majority of its priests, its Bishops, and finally Archbishop Lefebvre himself - the claim that the new rites are invalid. That is not a true claim, but more to the point here, it is not the position of the Society. There's an excellent article put out by the Angelus that is in this forum's library that establishes the validity of the rites, from theology, from Tradition, from history, from sacramental principles and from reason, done and approved by the SSPX priests and Bishops.
Regarding some of the actual criticisms the SSPX authorities make of St.Peter's, with respect to these which are more important, suffice to say St.Peter's believes their position is, on the whole, more consistent when all things are taken into account. There are two principal points of disagreement, and this is what was enlisted in the agreement of 1988, which Archbishop Lefebvre at least temporarily considered. That is, that the new rites are not invalid (which is not to say there are not other legitimate criticisms that can be made of them) and one regarding the Council itself in the light of Tradition.
Now, the FSSP is scorned mostly by independent groups, and the difficulties it has faced at times from the Roman authorities is said to be proof of its failure. But just by way of comparison, there was another group of a few priests, just like St.Peter's that split from the SSPX around the time, slightly earlier, than they did. This was the SSPV.
Now, by way of comparison, the FSSP since then now has about 200 priests and 150 seminarians, almost keeping pace with the historical growth rate of the SSPX, Fr.Borg said recently that they've helped since SP some 100 diocesan priests have offered the traditional Mass, have remained relatively scandal-free, and have many good and holy priests zealous for the salvation of souls orthodoxy in believing all that the Church has ever defined. This is rather better than the SSPV, all told, it seems to me. So the FSSP are a model that even without all the benefits that go with independence, it is at least not impossible to work for the good of the universal and Catholic Church in a canonically regular situation with the Holy and Apostolic See of St.Peter.