The joint approach, which is the simplest, takes advantage of Miriad's mosaicing software. In this case, all pointings are handled simultaneously by the imaging and deconvolution software. With the individual approach, a mosaic experiment is treated like a large number of conventional observations, where each pointing is imaged and deconvolved separately. In this case you, the user, are responsible for keeping track of all the pointings. Only as a final step are all the pointings pieced together.
The advantage of the joint approach is speed and simplicity. Also because the deconvolution of all the pointings is done together, it can produce fundamentally better deconvolutions. This is particularly so for low signal-to-noise ratio mosaics and for extended emission (emission comparable in extent to the primary beam - see Cornwell's papers for the argument). It is the approach normally used. However there are disadvantages - the joint approach depends more critically on the model of the primary beam. Errors in the model of the primary beam will tend to be amplified by this approach, particularly when the u-v coverage is poor. Generally the joint approach will be limited to dynamic ranges of several hundred or so.
A more practical difference between the two approaches is that the joint approach generally uses significantly less disk space (this can be an order of magnitude or more for spectral line experiments). However, because the joint approach does all pointings simultaneously, it does use significantly more computer memory in its reduction steps. With current computers, the joint approach is not possible for full resolution ATCA images (6 km array) if you have more that a few pointings.