According to Invitrogen pichia pastoris cloning system using pPIC vectors there is an option to insert into AOX1 or HIS4 when using GS115 or KM71 strains.

In both cases the SAME phenotype is generated so why insert into AOX1 or HIS4? What are advantages/disadvantages of using either/or?

Here is the description from Invitrogen word for word:

For insertion at AOX1 in GS115 or KM71, linearize with Sac I (generates His+ Mut+ in GS115 and His+ MutS in KM71)

For insertion at HIS4, linearize with Sal I (generates His+ Mut+ in GS115 and His+ MutS in KM71)