It's been suggested from the start that if they aren't friends now, they certainly were in the past. "The Sound of Drums"/"Last of the Time Lords" two-parter established they were friends as children. It has also been hinted at (in "Planet of Fire" and again in the Sounds/Last two-parter) that they could be related in some way. As far as their relationship with Master-as-villain, the Delgado Master's relationship with the Third Doctor and the Simm Master's relationship with the Tenth Doctor hints at a level mutual respect, at least. Sort of like how Holmes and Moriarty respected each other.
It is further established in both the Target Books novelisations and the Big Finish Audios that they were best friends as children and at the Academy. (This was supported by "The End of Time", in which they reminisced about their childhood, just before they discovered that the 4-beat sound in the Master's head was real.) The Doctor Who Magazine comic story Flashback sees the two having a major falling out while still on Gallifrey.