The benefit of first topstitching and then assembling or quilting is that the quilt can be stitched without stopping to constantly change threads, or skipping large areas. You simply quilt as desired using whatever thread is chosen and the project is a bit less technically challenged. Also with all the shifting, folding an stretching of fabrics you run no danger of a piece lifting or popping of the face of the quilt while quilting the final project.
The con is the applique work loses some of its definition and depth. This opinion is personal –some may not find the distinction ‘distinct enough’ to matter.
The benefit of ironing-on applique pieces, going to the trouble of pinning or basting them first then basting together quilt sandwich and quilt/applique at once is definitely about ‘the look’ for me. There is something slightly more 3 d that is visually appealing to this quilter.
The cons: Pieces may come loose and need to be touched up with the iron. The other is that you are stuck changing threads out constantly or are quilt/appliqueing sections and not quilting the bits in between at the same time. The large gaps in between would mean that (unless you have basted the sandwich well and kept your tension in your hands consistent) you may end up with areas that have wrinkles or poofy bits that are hard to quilt without causing pleats. Just being honest here. SO if trying this method close basting is necessary or changing threads lots.
If quilting after already sewing down the raw edge applique- this means essentially raw edge applique twice as you need to stitch down the pieces to the quilt body anyway or have a strange dynamic of the applique pieces sitting unevenly away from the backing. The initial stitching tends to flatten the applique pieces.
If combining quilting and stitching, you are actually doing something slightly more technically difficult, but the more 3d look is really my preferred method. Different quilts require different approaches and this is totally a matter of taste and which of the looks/challenges you prefer.