What is the main difference between ArcGIS Server 10.0 and 10.3?
What is the advantages of ArcGIS Server 10.3 over 10.0?
What is the main difference between ArcGIS Server 10.0 and 10.3?
What is the advantages of ArcGIS Server 10.3 over 10.0?
You are really looking for a difference between ArcGIS Server (AGS) 10 and 10.1 (there are almost no changes in 10.3 since 10.1 in terms of architecture).
Read this page from Esri Help: What's new in ArcGIS 10.1 for Server. This will give you a good overview of the difference. There are dozens of Esri videos on the new AGS 10.1 introduced around in 2010.
ArcGIS for Server Product Life Cycle Support Status document will give you a good understanding of why you should not work with AGS 10.0 (it will be retired in 6 months) and should really start with AGS 10.3.1 (the latest release).
Just forget that the AGS 10 ever existed and start working with AGS 10.3 (unless you are already maintaining an AGS 10 site and looking for the upgrade oportunities). In this case, there is a great Help page (and classroom training) for migrating to 10.1+ from 10.