Memory isn't the only question ... performance is a dynamic between CPU speed (speed of the main computer processor), bus (how fast the computer can talk to its components), system memory & speed, GPU speed and GPU memory & speed. In general the faster the CPU/GPU/bus/memory the better the computer can render the game. But some faster components have slower architecture (ie, how the small bits of the chips are arranged) meaning they compute slowly when compared to a more efficient slower chip.
Having more memory helps ... to a point where there is no bottleneck with the CPU/GPU/bus speed/architecture.
In general the more you spend the better (usually). You bought a very cheap GPU and therefore have slow performance. Adding to this you bought an GPU a generation older than the one it replaced.
(I've tried to write the above in simple terms and therefore using a broad brush to explain a complex subject.)