They both have to be USB 3. It uses a different hardware chip.
External USB hard drives are not all manufactured the same way, however since you state yours are "large", there is a very good chance that if you were to take your enclosures apart (normally destroying the enclosure, but not destroying the drives inside) you would find a normal 3.5" hard drive bundled with a SATA to USB 2.0 adapter. And, if that is how your enclosure(s) were constructed, you could remove the drives from your existing enclosures and purchase new external drive enclosures that support USB 3.0 that would give these drives a new high-speed lease on life! The enclosures made for 3.5" drives that support USB 3.0 run from about $25 to $45, so this could be a very attractive option for you. Too, your data should still be on the drives themselves and should not need reformatting.
Finally, if anyone is reading this that has an external hard drive that is smaller (not capacity, I mean physically built using a 2.5" drive as opposed to a 3.5" drive), then most of these devices now are specially built and do not have drives with SATA connections on them. So, make sure your model has a "normal" drive in it (Google how to open your model of enclosure to learn more), before you start any surgical procedures .
As Jim said not all USB interfaces are the same quality. Look at the reviews to see that owners are satisfied with good performance. USB3 generally is a faster interface than most hard drives, but they will limit a good SSD's performance.