The 5D will get better details than the 1.6 crop. A macro lens will resolve a certain number of line pairs per millimetre. Image sharpness is measured in line pairs per picture height, by using the same lens but with physically bigger sensor you will get more line pairs per picture height, hence more detail in your image.
Another way to look at it is that using a smaller sensor is like making an enlargement, or viewing a portion of an image close up - it's never going to look as sharp under those circumstances.
Now on some lenses corner performance can drop off to the extent that you get better average sharpness (but lower peak sharpness) by using a crop sensor and simply avoiding the extreme corners. Here is an example of such a lens, the Canon 35mm f/2.0:
APS-C corners occur at 13.5mm, where sharpness at f/8.0 (fine blue line) remains above 0.8. On full frame sharpness takes a nose dive starting at 18mm, which corresponds to middle of the left or right edge of the frame. Now compare that to the Canon 180mm f/3.5L Macro:
Sharpness is extremely high right across the frame, there is no notable drop off, meaning your full frame image will be sharper everywhere, even in the extreme corners.
However if both cameras have a similar same number of megapixels then a crop sensor can be very useful for macro photography as it allows you to photograph smaller objects. A true macro lens on full frame will let you fill the frame with an object only 36mm across, whearas with a crop camera you can fill the [1.6x smaller] frame with an object only 22.5mm across. This can be very useful for um, photographing really small things!