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The ArcGIS Network Analyst's Route solver with the FindBestSequence option returns a different solution than solving the same problem using ArcView 3.x Network Analyst.
ArcGIS Network Analyst uses a different algorithm than ArcView 3.x. Unlike ArcView 3.x's algorithm, the new algorithm in ArcGIS Network Analyst computes a tour solution taking into account time window constraints at the stops. Since the algorithm is different, then the results may be different.
Both ArcGIS Network Analyst's Route solver with the FindBestSequence option, and ArcView 3.x Network Analyst solves the well-known Traveling Salesman Problem (TSP). In order to solve TSP, a heuristic approach has been implemented for both software programs. These heuristic approaches provide good trade-offs between tour quality and computation time. However, neither of these approaches guarantee to find the optimal solution.
Since both TSP algorithms use heuristic approaches, the routes returned by the Route solver and by ArcView 3.x Network Analyst are not guaranteed to be optimal.