I, to, would like an easy means to do what the OP asked. Ideally, it should spit the contents of the Vortex "MODS" display to a text file using the same filters and sort order selected for the display. The fields would be separated by tabs to allow easy import to a spreadsheet.
This would allow me to answer questions like "How is profile X different from profile Y" by feeding the text output of each into WinMerge.
As to the following suggestion:
I knocked this up a minute ago, you can do this, or a variation of it in Powershell;
cd <your mods directory>
Get-ChildItem -Recurse | Select-Object -ExpandProperty Fullname | Out-File <your mods directory>\mymodfile.txt
This produces a list of every file under <your mods directory> including all the contents of the folders and subfolders.
From ...\Vortex\skyrim\mods it lists every from every mod installed (according to Vortex), including those not enabled.
From ...\Skyrim\data it lists every file installed in Skyrim.
Neither is what the OP is asking for, which is, most likely, the "MODS" display of Vortex converted to text, Ideally filtered by, for example, "Status: Enabled".
The best you can do with Powershell is get a list of all possibly installed mods (or rather the archive name, which is usually close) with:
get-childitem | select-object -expandproperty name
Then you would have to edit the file and remove lines corresponding to mods which are not "Status: Enabled" in the left column of the mods page. This at least saves a lot of typing, but is still laborious.