I think that at least two of Scrivener’s tools may help you on this process: snapshots and revision modes. The first one will allow easy comparison with your previous version an the second one will allow you to identify different edits phases.
I suggest you to go through the manual sections 15.6 Using Snapshots and 18.5 Marking Revisions.
Personally, I don’t find it helpful to compare drafts. I prefer to “live in the moment” of how the text reads now, rather than jumping back and forth between versions. And so I don’t really use revision marks and snapshots unless a client wants them. Other people swear by those features and wouldn’t dare edit without them. YMMV.
OTOH, extra backups are never bad. That way, if you decide that whatever approach you choose is disastrously bad, you can give yourself a “do-over.”
When I am done with my first draft, I will make a copy of the entire .Scriv folder and rename it to “Project FIRST DRAFT”.
I will then continue to make my second draft revisions in the original project. In the event I need to compare to the original draft, it seems easy enough to me to just launch that in Scrivener and compare the versions side by side.
That’s how I would do it In windows, not sure how things work on the mac.
It would work similarly on the Mac, except that the .scriv folder just looks like a file there. I suggest that instead of copying the folder, go ahead and use File->Backup->Backup to…, which gives you the option to .zip compress the backup, so there’s no confusion which one is the one you intend to work on (the original).
A third option no one has mentioned is to select the Draft/Manuscript/whatever folder and use the function Documents->Duplicate->with Subdocuments… That should produce a copy of the folder and all its contents, which you can rename to “1st draft” and also move it to another spot, such as Research or the like. Handy for comparing side-by-side, though you’ll want to do something to distinguish the 1st draft from the rest, such as coloring all the 1st draft text, and maybe creating snapshots of all the documents in case you accidentally edit them.
A 4th option is to compile the 1st draft to PDF and re-import that for reference, which will prevent accidental editing. Enabling titles & maybe even synopses in the Formatting pane of compile might be a good idea here.