You're talking about the speed of copying the files from one partition to another?
As TwoBoxer suggested, it depends on how far apart the files are physically stored on the disk. That's true whether they're in two partitions or in the same partition, although it's more likely that they're further apart (and therefore copy more slowly) when you have two partitions.
If the existing files are at the very end of the 1st partition, and if they're being copied to the very beginning of the 2nd partition, then they'll be physically close together on the drive and the copy will be as fast as it can be for a single disk (which will still be a lot slower than if you're copying from one physical disk to another).
But on average, files will be located in the middle of the partitions and therefore the head will have to seek a distance that's half the combined partition sizes - that will make the copy much slower.
If the files are small, though, then write caching will improve performance considerably. If the files being copied can fit entirely into the file system's RAM cache then the copy speed could be as fast as between two separate drives.