In my opinion, the advantages of a JMP Report over a JMP Journal, or the advantages of a JMP Journal over a JMP Report, boils down to the underlying makeup of them.
A JMP Report is actually a JSL script with typically the data table used by the script embedded in it. When a file with the .jrp extension is opened, JMP automatically runs the embedded script. So you end up back where you were when you saved the report. That is, as long as you chose to embed the data table in the report, or when you open the report, the data table has been opened in your JMP session. The displayed output is there, as well as the data for it. You can modify select the red triangle options, etc. And if you pass a .jrp to another person, when they open it up, they now have a copy of your data too.
A JMP journal is a copy of the report output. Here the journal can be built from many different items from different reports that are based upon analyses from different data tables. Once saved, what you have is a replica of the created output. When you reopen the file, you will see the output from the analysis, however, you do not have the ability to use any of the analytical or display actions available under the red triangles that are there when the analytical or graphical platform was originally run.
So to me, each of them has their own advantages and disadvantages. I use them based upon what I will need when the report or journal is opened up.
Jim