Why does the battery eliminator connected to the wall provide a better spin to my dc motors than my battery of the same voltage?
First off, never use 9V batteries to power motors or any device that consumes more than a few hundreds mA. Those batteries are just too weak.

Now a battery eliminator is not a pure equivalent as it can typically supply 800 mA or more, depending on the model you get.

The only commonalities between the battery and the eliminator are the 9V voltage and the socket.

If you want to power DC motors with batteries then rather use several 1.5V batteries in series.