Just a couple of things from me:
As far as transferring the data from one external HD to another it is really just a matter of plugging them both in and using Drag & Drop from one to the other. This method will remove the file from one HD and transfer it to the other or if you wish to keep both copies (which I suggest is safer) you could clone the smaller drive to the new, larger drive using my favorite cloning software Carbon Copy Cloner (CCC). You can also select which specific folders to clone.
Regarding duplicates, that's a bit tricky. There are a lot of third party app's that will allow you to search for and remove duplicates, some are specific for photos, others include all data types. Duplicate Fixer and it's Pro version will allow you to search specific Photo Libraries whereas Gemini 2 will allow you to search for all file types but both cost money and the down side is that you can't compare files from the Mac HD with files on an Ext HD automatically.
This is why I no longer suggest people copy their Photos library to an external HD unless it is due to space limitations and they intend to use it as their default library. If it's just a backup it becomes very difficult to keep the two in sync after a short time.
By far the easiest way to ensure that your backup stays in sync is to clone the entire Mac HD to an external HD and update it on a regular (I use weekly) basis.
With CCC you also get a "Safety Net" for files you may have deleted on the source accidentally.
CCC (and some other cloning software) also creates a bootable clone meaning you can run your device from it in the event of internal drive failure or repair it where possible. Very handy for Restoring your old computer to a new device or new HD too.
For my money (CCC is about $50.00) is well worth the cost and peace of mind.
Lastly you can get a free, fully functional, 30 day trial version to test out.