I didn't think Clapton played with a Pignose until the 461 Ocean Boulevard album (listen to Motherless Children, as a great example of a Pignose).
It's a little "drier" sounding to me than a Champ, which has a strong "tube" distortion. Of course, I could be wrong.
BTW, Page of course picked up the les paul in the studio on II and III, but didn't necessarily always record with it after that (much of Presence was with a Strat, for example).
Interesting fact: don't know who the children were on Houses of the Holy, but there were actually only 2 them photographed several times!