There are a several options; it depends a bit on the original’s size:
IF you have two images that are IDENTICAL IN SIZE:
1) drag and drop the layer you want to copy to the other file INSIDE the actual contents: dropped on the spot where you drop it
2) drag and drop the layer you want to copy to the other file OUTSIDE the boundaries (grey area): same x and y coordinates are maintained (you will have to zoom out and have the surrounding grey visible for this to work)
3) drag and drop the layer you want to copy to the other file INSIDE the actual contents WHILE holding <SHIFT>: same x and y coordinates are maintained
4) <CTRL>-CLICK on the icon of the layer you wish to copy, copy <CTRL><C> and paste <CTRL><V>in the other file: layer is copied to exact CENTER
IF you have two images that DIFFER IN SIZE:
1) drag and drop the layer you want to copy to the other file INSIDE the actual contents: dropped on the spot where you drop it
2) drag and drop the layer you want to copy to the other file OUTSIDE the boundaries (grey area): layer is copied to exact CENTER of the page (you will have to zoom out and have the surrounding grey visible for this to work)
3) drag and drop the layer you want to copy to the other file INSIDE the actual contents WHILE holding <SHIFT>: layer is copied to exact CENTER of the page
4) select the layer you want to copy; open the flyout menu of the layer palette (top right button) and choose "Duplicate Layer". A dialog pops up - select the image to copy to in the drop down list and hit OK. If the second image is LARGER: same x and y coordinates are maintained. If SMALLER: same behaviour, HOWEVER it will be placed OUTSIDE the visible area.
For mac, hold down the <COMMAND> instead of <CTRL>. When dragging and dropping, it doesn't really matter whether you drag the actual layer or the contents of the layer (AFAIK). Point of reference (0,0) is always top left.
Should you need more control, try these:
Image-->Apply Image : lots of different duplication effects possible
Image-->Calculations: easy channel duplication between files.
There are possibly other methods, but these I remember of the top of my hat.
Edit: <CTRL><J> only works within the same file, not for copying layers to other files.