I doubt that we have enough information to answer your question. Long running operations are typically "bound" by one of three factors: CPU speed, memory, or disk i/o. An operation that's CPU bound won't be significantly speeded up by adding more memory. You have to address the factor that's causing the bottleneck.
In your case it's a good bet that your operation is i/o bound. That's just a guess, but if it's true I would expect the copy to take about the same time on the faster computer.