Despite the misinformation presented here all but the very fastest micro SD cards are not going to be limited by USB 2.0, and even if they are it's only by a factor of 2-3x under absolutely ideal circumstances. In the vast majority of cases with consumer grade flash the controller/flash in the SD card itself are going to be limitations long before USB 2.0 is a problem.
That said, ElFenix is on to something - How are you connecting everything here? Use cables, make sure that everything is working at the speeds you expect.
I've got a work laptop with a built-in SD card reader that I can borrow over the weekend, and the the new 256 GB card came with an adapter anyways, so I could at least take out the old SD card, and copy everything over, then pop in the new SD card and then copy it onto there.
Surely that's much faster, no?
Maybe. Pulling the card out of the phone will eliminate potential weirdness on the data path between phone and PC and is going to give you the most pure shot at being flash limited. That's certainly the ideal way to do it if you aren't 100% confident in the performance of the phone as a reader.
For further help:
What SD cards are you using (exact models)? Are you sure they are genuine?
What reader hardware, and what interface does it use to connect? Are you sure everything is operating at the optimum speed?
What type of files are you dealing with here? Mostly I mean size, but type could give us a clue as to size eg is it a card full of movies or did you install apps to the card and it's full of tiny little application components.
Small files have lots of OS overhead and punish low grade flash and controllers. Low single digit MB/s is not uncommon at all even on mid-grade cards with moderate 50-60 MB/s sequential ratings.
Viper GTS