The official original XBOX controllers, both the S and the Duke, are common ground controllers. Most 3rd party or knockoff XBOX controllers are Common Ground also. If you're using something there that has voltage for the common line, and/or some weird layout, then you'll need to use switch ICs as micro has suggested. The 4066 are great for that, then also as mentioned you'd want a couple of CD4049 Inverting Buffer ICs and pull-ups on every button line of the NeoGeo.
You could use the much smaller 74LVC1G384, as it is an active Lo Bilateral switch, but you would need to make up a PCB for them and still use pull-ups. After you built something like that up, then you could wire up really any controller that has just switches/buttons in it to any other active controller you wanted, regardless of it's button layout. I made this up just tinkering with the idea after seeing this post, It only does at most 10 buttons, but it could be expanded or shrunk as needed, and as shown there it's roughly only 30mm x 30mm with 2.54mm headers. http://www.nxp.com/documents/data_sheet/74LVC1G384.pdf
On an XBOX 360 note:
The official 360 controllers have 3 different main layouts, Matrix, CL and CG. The Wired controller has 2 versions, then the Wireless has 5 versions.
Wired Matrix, first ones that were released. The buttons are in a Matrix layout. The Triggers go Lo to activate.
Wired CL, latest and mostly what are out now for new ones. The buttons use a Common Line, 1.8v for all of them. The Triggers go Lo to activate.
Wireless Matrix, first ones that were released. The buttons are in a Matrix layout. The Triggers got Lo to activate.
Wireless CG, CG2 and CG3, all buttons are in a Common Ground layout. The Triggers go Hi (1.6v) to activate.
Wireless Matrix 2, latest version, buttons back to a Matrix layout. Triggers go Lo to activate.