All else being equal, a newer, larger hard drive is generally faster than an older, smaller one. That's because the bits are packed more densely - they can read/write more bits on each revolution.
For drives of the same generation, where capacity differences are more likely due to the number of heads/platters, the reason is a bit different. There, there's no difference in how fast the bits can be read. But larger would still be faster since there's more bits on each track, so less stepping (seek time) when reading the same amount of data.
Any reasonable SSD will be much faster.
