Shimano XT 10 speed rear derailleurs have come in at least three different bracket axle units. The units and mounting bolts are not cross compatible. Here's a summary of the situation:
RD-M773 - 10 speed "Shadow" rear derailleur
Has a narrow bracket axle unit with a mounting bolt that is 5mm in diameter on the end.
Amazon have replacement bracket axle units for about $8.
RD-M780 - 10 speed "Shadow" rear derailleur
Has a wide bracket axle unit with a mounting bolt that is 5mm in diameter on the end.
Small 5mm hole:
I can't seem to find a specific replacement for
RD-M786 - 10 speed "Shadow+" rear derailleur
Has a wide bracket axle unit with a mounting bolt that is 8mm in diameter on the end.
Large 8mm hole:
The bracket axle units for the RD-M786 seem to be the same as for the RD-M781 (OEM XT Shadow+ rear derailleur) and the SLX and Deore Shadow+ rear derailleurs (RD-M675, RD-M670 and RD-M610) see this Amazon listing.
Small and large mounting bolts compared
Bracket axle units compared
Why the changes?
The first two derailleurs are Shadow (non-clutch type). The RD-M773 had a steel bracket axle unit that was stronger than the aluminium versi0n, so it did not need to be as wide. When Shimano went to the M780, they went with an aluminium bracket axle unit like on the XTR derailleurs, but in doing so had to go wider to accomodate the reduction in strength associated with going to aluminium.
The RD-M786 is a Shadow+ (clutch) type derailleur. The clutch puts a lot more force on the derailleur and so it seems that although Shimano retained the same width aluminium bracket axle unit, they upped the bolt diameter to make the mount stronger.