According to JP himself, the main amp for dirty stuff on BC&SL was a Mark IIC+ (modded ++ according to some), but he also used a Mark IV for some parts. Towards the end of the recording he got the new Mark V and used it for rhythm in some places and most notably the outro solo in "The Count of Tuscany".
The main clean amp was most probably a Lonestar, since that is what he had been using live and on two records before that.
JP mostly uses stock Mesa 6L6 powertubes, except for a brief time using the EL34/6L6 combo in his Mark IV´s on the Systematic Chaos tour.