They use different programming algorithms.
The AVR is actually simpler to program. Making a PIC specific programmer work with AVR would not be a fun task.
Making a PIC and AVR programmer as a new project with very few parts is possible.
You can even program an AVR with a parallel port and 3 resistors, although it is not the safest programmer.
You might want to look at: http://www.lancos.com/prog.html
Not very expensive for parts... free software.
If you have a PICKIT programmer... then you only have a programmer that can program PICs.
Dataman programmers can program AVR's with the right adapters.