Quick pros/cons from what I've read (correct me if I'm wrong - I've not used syncthing myself):
syncthing
Pros:
- Easy to setup and use.
- No infrastructure to maintain
- Will sync directories between computers
Cons:
- Uses third party resources to sync by default (can setup direct sync if needed/wanted however)
- Only does directory synchronization
Nextcloud
Pros:
- Can synchronize directories
- Entire synchronization pipeline is under your control
- Offers a lot more functionality if you want it (WebDAV, Calendars, public shares with "anyone with URL can view" permission, etc.)
Cons:
- You need to setup/maintain your Nextcloud server
- Can be fiddly to setup for some (wasn't for me - but lots of people do complain about it).