Indeed, this aspect of presenting visible signs of continuity was indeed something that was very purposeful on the part of Benedict XVI, for just as one might use symbols to signal rupture or novelty, likewise symbols can also be used to signal continuity. But while these vestments are frequently shown, little more about them is said, so in view of that, I thought it might be of interest to break down what the pontiff is wearing and from whence it came.
The precious mitre shown here comes from the pontificate of Pope Benedict XV (note: the fifteenth, not the sixteenth) who reigned as pope from 1914-1922.
This particular mitre, notable for its exquisite design, was one that Pius XII would also frequently be found to wear -- and in point of fact, it is this mitre which he is shown wearing in the statue of him in St. Peter's Basilica:
Which then brings us full circle back to Benedict XVI.
As for the cope the pope chose to wear on this occasion, it was originally a full-fledged papal mantum (effectively a cope with a longer train that, at one time, was worn by other prelates beyond the person of the pope). This particular mantum comes from the pontificate of Pope John XXIII who stemma can be found on the base of the orphreys.
In actuality, two such were made during the pontificate of John XXIII, the white one shown here, and another in red:
These were made by the Sisters of San Giuseppe al Lungotevere Farnesina located near the Vatican. The embroidery is set silk lamé and includes golden embroideries in a candelabra motif inclusive of floriated vines. Stylized lilies (i.e. the fleur-de-lys) adorn the entire body of the cope and also part of the design of the embroidered galloons.
The white version of this mantum -- which was only completed by the sisters following the death of John XXIII and so was never used by him. Paul VI wore it as a mantum in the earlier years of his pontificate, but it would eventually be reduced in length during the pontificate of John Paul II who also used it as a cope on at least one occasion.