There is a difference with using a macro lens on a fullframe camera body as opposed to a crop sensor camera body. This difference for some is seen as an advantage - by other as a disadvantage and some just don't care - it depends what they are after.
Simply put first understand what true macro (1:1) is. True macro is when the image reflected on the camera sensor by the lens is the same size as the subject is in real life (1:1). So a 5mm insect will be reflected as a 5mm image on the sensor. This means that true macro as achieved with any true macro lens will always give the same frame cover (when focused at its closest focusing point) no matter its focal length - so a 60mm macro and a 200mm macro lens will give you the same frame of the subject - the difference being that the 60mm will be physically closer to the subject than the 200mm lens will be.
In addition to this the depth of field (as far as I know) will be the same for each shot (or if there is any difference its so marginal as to be irrelevant), however the longer focal length lenses will render a greater degree of blurring to background areas of the shot.
Now lets bring sensor size into the mix - clearly because of what true macro is if you use a larger sensor size you will capture more frame coverage of the subject than if you were using a smaller sensor. This means that for two camera sensors of similar MP ratings when you print the final result the crop sensor shot will appear to have more magnification than the fullframe because the cropped image has been blown up to the same print size. This gets more confusing as you get higher MP rated fullframe sensors with the increased capacity to crop the shots.
Secondly the size of the sensor will affect the circle of confusion which in turn means that two key properties will be different. Between the typical 1.6crop sensor DSLR and the fullframe DSLR sensor (35mm) the crop sensor gains about one stops worth in aperture of depth of field over the fullframe camera sensor. However in turn the crop sensor has the diffraction* effect kick in about one stop earlier than fullframe. So as a result the two somewhat cancel each other out since the fullframe sensor can be used at a smaller aperture to get the "lost" depth of field back.
* the effect of softening on a shot no matter how well its taken. It tends to start taking effect after f8 and continues to soften shots progressively as you stop the aperture down further. The specific point at which it becomes too soft for general use is highly dependant upon the camera body; lens; output use of the photo and the photographers own quality demands. Generally speaking you start to see the effect by f10, but on 1.6 crop it won't start to be a major problem till around f16 (thus for most f13 is the accepted smallest aperture whilst retaining good image quality).
On fullframe the 1 extra stop shifts the numbers to f16 as the accepted smallest and f22 as the point where it starts to kick in.
Thus in short macro is 100% possible on a 1.6 crop DSLR and a great many macro shooters use crop sensors without a problem - in fact I would say the majority are quite happy working today with 1.6 crop camera bodies. That said there are those that happily use fullframe and even those that use medium and large formate camera bodies to get their macro shots.
Generally speaking though the advantage/disadvantage is only relevant if you have prior experience of working with fullframe camera bodies or are after a specific effect/shot that only those bodies can achieve.
Tools of the trade: Canon 400D, Canon 7D, Canon 70-200mm f2.8 IS L M2, Sigma 120-300mm f2.8 OS, Canon MPE 65mm f2.8 macro, Sigma 150mm f2.8 macro, Tamron 24-70mm f2.4, Sigma 70mm f2.8 macro, Sigma 8-16mm f4.5-5.6, Raynox DCR 250, loads of teleconverters and a flashy thingy too