Hi Alex,
> Do you recommend ArcGIS Online or ArcGIS Server?
I think a more accurate comparison would be: should you use ArcGIS Online or Portal for ArcGIS? The former is an Esri hosted cloud-based solution, and the latter is an on-premises solution that your organization would host (either on physical machines or your own private cloud). Some reasons why you would select one over the other:
> If using ArcGIS Server, how do I connect inspectors for track editors since they are non- GIS users?
Not 100% sure what you're asking here. You can have your data in an enterprise (i.e., ArcSDE) geodatabase, share the data out as feature services via ArcGIS Server, then use Portal for ArcGIS as a front end for your Collector for ArcGIS app to connect to and access - to support your editing workflows. The inspectors would need to be named users who can sign into your Portal for ArcGIS instance.
> If using ArcGIS Online hosted feature services, can it connect to SDE geodatabase directly?
Yes, this workflow is possible. You can have your data in an enterprise (i.e., ArcSDE) geodatabase, share the data out as feature services via ArcGIS Server, then register these feature services with ArcGIS Online. Collector for ArcGIS can connect to and access your ArcGIS Online organization, then edit the feature services. Again, the inspectors would need to be named users in your ArcGIS Online organization.
FYI for more background please review the contents of this whitepaper,
https://community.esri.com/groups/mobile-gis/blog/2017/10/25/arcgis-secure-mobile-implementation-pat...
Specifically section 5 which discusses some of the pros/cons of different mobile deployment patterns and the security considerations.
Hope this helps,