This discussion makes not much sense when you compare both algorhithms. Basically Dijkstra and A* are the same. The only difference is one estimation function that you have to add to Dijkstra and you will automatically get A*. So it will not calculate each possible route on a node, it will estimate with a function where to go to find the shortest route to the goal node. Often they simply use a length-function (length between current node and goal) for that.

So if you have Dijkstra, than you almost have A*. And if you have A*, then Dijkstra is already implemented. You only have to remove this estimation function.

But when you want to calculate all routes in a tree (for each node to each possible node), then you have to use Dijkstra. This makes sense, when you pre-calculate a matrix. With such a matrix you dont have to calculate routes in real-time. You just look them up from this pre-calculated matrix. I thought this is the way Intense-X pathfinding works.

You can find more details on this here:
http://www.amazon.com/Programming-Game-Example-Mat-Buckland/dp/1556220782