Identifying Grey-headed and Pacific (Buller's) Albatrosses on the Water
Upper - immatures, original photo size 100%
Lower - immatures, photo size increased to 115%
Edward Soldaat sent a plate from Murphy's 'Oceanic Birds of South America' (1936). This shows drawings of the bills of five species of albatross. Numbers 2 and 3 from the top are Buller's and Grey-headed - note that the nostrils, fleshy parts, base of culminicorn and shape of cutting edge are different between these two taxa.
Right - Bills of Mollymawks. Lateral and dorsal aspects of five species, based upon specimens in the Brewster-Sanford and America Museum collections, to illustrate the form of the plates and of the integument in the commisures, and the distribution of colour. Reading from the top downward:
D. melanophris (Corral, Chile)
D. bulleri (Valapraiseo, Chile)
D. chrysostoma (South Georgia)
D. chlororhynchos (South Atlantic)
D. cauta salvini (South Pacific)
The relevant drawings have been juxtaposed on the photos at the top of the page - the nostrils can be seen, as can the cutting edge (incidentally proving correct identification of both birds). These differences in the bill plates may be valuable at close range with good visibility.
 
However the following would be of more practical use in the field. Peter Harrison notes that in 'Bullerís' the head is always proportionally larger with a higher crown peak that peaks further behind the eye when compared with Grey-headed. He says that the real clincher between these two species though, is the length of the jowl line (look at the 'length of the chin' between the two species above - the Grey-headed chin length is much shorter than that of Bullerís, giving Bullerís a distinctive heavy jowled and larger-headed appearance than Grey-headed). According to PH, with practice this difference in jizz allows separation at a glance when the two species are sitting on the water.

Peter kindly sent the sketch below to illustrate his point:
Peter Burke noted also the placement of the eye in relation to the bill. On Bullerís it is closer and higher up, so that it comes off the top of the culmen at a straight line. The photos of Grey-headed seem to show the eye further back and down from the top of the culmen. However the two photos may have been taken from different angles, and there may be the effect of shadowing.

PB also noted that the throat and chin of Bullerís seems to be longer, giving the face a longer look than Grey-headed (latter comment, as per Peter Harrison)
In summary:

(1) The length of the chin and throat (the jowl) will identify the two species at all ages - this would have effectively ruled out Grey-headed in the earlier puzzle (WhichAlbatross.html). I believe this is new unpublished information

(2) If the bill plates can be seen, the pattern would identify the species

(3) Check position of eye (qualify as a new field character)

(4) Note peak of crown to eye position