Note: I'm assuming you are using the built-in StreetMap North America dataset that comes with ArcGIS to perform your network analyses.
There are two factors that may be influencing your service areas created with Network Analyst: hierarchical analysis and polygon type.
- Hierarchical analysis is a heuristic method for solving drive time by favoring travel on larger roads (e.g. highways) over small roads (e.g. local streets). Network Analyst can compute service areas more quickly when using a Hierarchical analysis, but it is less exhaustive than a non-hierarchical analysis. The About network analysis with hierarchy help page has more info. Although hierarchical analysis is performed by default, you can disable it: right click your service areas layer in the table of contents, go to "Layer Properties", then to "Analysis Settings" tab, then toggle "Use Hierarchy" (see below).
- Polygon Type is a setting that specifies how detailed the resulting service area polygons should be. By default, "generalized" polygons are created where enclaves of unreachable territory are iteratively filled in. By changing the polygon type, "detailed" polygons can be created that perform no filling, but require significantly more processing time. To modify this setting, right click your service areas layer in the table of contents, go to "Layer Properties", then to "Polygon Generation" tab, then toggle "Use Hierarchy" (see below).
Note that when performing a hierarchical analysis, you must use generalized polygons. In a non-hierarchical analysis, you can use either generalized or detailed polygons.