compare two hex files
The lines in a typical hex file include a VLI (variable length indicator). The hex files output from the IDE might have different lengths than those produced by avrdude. As a simple example:

File 1:

03ABC
03DEF


File 2:

06ABCDEF


Those files will compare differently to each other but convey the same information, split differently between lines.

To do a genuine comparison you would need to account for that.


  Board Type? 


Different boards, but with the same processor, might have identical files.


  Microprocessor type?


Different processor would almost certainly have different hex files.


  avrdude version?


Probably not, however see my comments above about the VLIs.


  anything else?


As I said, the compiler may generate lines with (say) 16 bytes per line, but avrdude might read back lines with 32 bytes per line. Thus they would look different but convey the same hex codes, once you allow for that.