I thought this problem might be related to the 1000 feature maximum import to shapefiles described in this thread, but the solution listed there is to create a map service.
So, why does the second webmap limit my displayed features? The only difference I can see is how the data are brought in.
In one web map, you've added the individual layers of an ArcGIS Server map service to the web map. By doing so, you are effectively accessing the layers like a feature service. The web map sends a query to the service to retrieve the geometry and attributes of the features and the client application draws them. So it works identically to how a feature service works and is limited to the number of features the client can draw.
In your other web map, you've added the entire map service. In this case, the web map sends a request to the service and the service draws all the layers and creates an image representation that the client then displays, sometimes transparently.
In one web map, you've added the individual layers of an ArcGIS Server map service to the web map. By doing so, you are effectively accessing the layers like a feature service. The web map sends a query to the service to retrieve the geometry and attributes of the features and the client application draws them. So it works identically to how a feature service works and is limited to the number of features the client can draw.
In your other web map, you've added the entire map service. In this case, the web map sends a request to the service and the service draws all the layers and creates an image representation that the client then displays, sometimes transparently.
