A* without heuristic more efficient than Dijkstra
It depends how you implement Dijkstra.  The usual description of Dijkstra adds every vertex of the graph to the queue at the start, which is rather inefficient.  A* without a heuristic is often called "uniform cost search" (UCS) and the way it's described, you only add vertices to the queue when you discover them.

This means that, especially in sparse graphs (such as road maps, which are almost planar), UCS has a much lower memory footprint, which can make it considerably faster.  Also, the various operations on the queue are much faster, since the queue is typically much shorter.

There's more information in Ariel Felner's paper Dijkstra's algorithm versus uniform cost search or a case against Dijkstra's algorithm (Proceedings of 4th International Symposium on Combinatorial Search, SoCS-2011, AAAI, 2011).

By the way, straight-line distance is probably a very good heuristic for A* in your situation.