Microsoft Consoles

todo: Add video links or website links showing detailed instructions.

Xbox Original

Similar cart sizes?	They're DVD so yes.
Can a PAL console be modified to function or even match NTSC speeds?	Certain PAL games have PAL60 mode but launch titles like PAL Halo 1 only runs at 50hz.
Method (Boot disk from an official game)	A Save file exploit of James Bond: Agent Under Fire or Tom Clancy's Splinter Cell Follow the instructions from the link and install UnleashX to enable imports Click here
Method (Modchip)	Various Xbox modchips, a small note that some require soldering and there's a good chance that some are only available for certain motherboard revisions.
Safe to use NTSC import consoles with official EU/UK power supply in Europe/UK?	Unknown

Similar DVD sizes?	Yes.
Can a PAL console be modified to function or even match NTSC speeds?	The majority of PAL Xbox 360 games runs at 60hz by default except for Hitman HD Collection......
Method (Retail DVD: Zero effort)	Have a look at the link to find out. It looks like that most Japan copies are locked to NTSC-J consoles Click here
Method (Xbox Live Arcade related import)	To be added soon, apparently it has something to do with making a Xbox account outside of the native country. A small note that a jtagged Xbox 360 isn't safe to connect online as Microsoft will ban the console limiting its uses completely.
Safe to use NTSC import consoles with official EU/UK power supply in Europe/UK?	Very likely no because the 360 power brick connector cannot fit into consoles outside of its native region.

Xbox 360 notes
Todo: Add info on possible DLC restrictions.

Similar Physical media sizes?	Yes.
Can a PAL console be modified to function or even match NTSC speeds?	It was confirmed before the release of Xbox One that the console is region free and every PAL released game is 60hz. Don't expect any special imports that is exclusive to Japan as that console is not doing well at all.
Safe to use NTSC import consoles with official EU/UK power supply in Europe/UK?	To be added later

Xbox One notes
Todo: Add info on possible DLC restrictions.