Here is my personal view of pros and cons.
with "alert", you can drill down to the detail in 2 clicks. Once on the main "home" or "pipeline alerts" tab on the main console, then click on the actual alert. However, the "alert" title can't show any variable values. If you have 20 calls coming in, you have an "alert" that shows "id", then the subject of all those alerts will all show "id". You have to drill down to see the detail.
With report, you can put a key value, and report main page will show the entry with the actual value of the "id" from your payload. The good thing is you can see multiple entries with different ID's. However, in order to see the detail, you have to drill it twice more. Click on the "id" entry, then click on the "details" to see more.
Here is an example of my report entry:
I have a payload body looks like:
in my report, I can add expression like $body, then above payload will show in the "detail" link. I can also add a key "pid". Look closely, "pid" is an actual element inside the payload, then in the value section, i put in path as "ins:CisPidsRtCollection/ins:CisPidsRt/ins:pid", and variable as "body", then the report entry will show "pid=123".