First, minor correction:
As emerging economies continue to expand, their energy needs are set to grow dramatically.
I assume you meant expand here, as you wrote in your second sentence. Expend word here would make the clause turn into "As emerging economies continue to expend their energy", but the rest doesn't make a complete sentence.
So what's the difference between:
As emerging economies continue to expand, their energy needs are set
to grow dramatically
The more emerging economies continue to expand, the more their energy
needs are set to grow dramatically
While both establish a relationship, I would argue that the first sets a very general trend. The growth of economy implies growth of energy needs.
The second would seem to imply a mathematical trend (linear, exponential, or otherwise). Of course, don't get me wrong, neither one is giving figures or data to support this claim, but in let's say that the latter case would suggest that such a relationship can be established between the two.
If you wanted to go further, you might say something like:
The energy needs of an economy is directly proportional to its growth.