Theoretically speaking, the answer would be:
Six of one; half-dozen of another.
The reason is, if you reach a bandwidth bottleneck, it doesn't matter if you are uploading files one at a time or multiple at once; you are constrained by bandwidth.
What alters the answer is if there's an imposed speed limit for connections on one side. This is seen on some regular content servers as well as those that use Torrenting protocol.
In this case, if the imposed speed limit is less than the max bandwidth on the home side, then it would make sense to transfer multiple files, up to the amount to cap out bandwidth on the home side.