error -36 is an I/O error and can occur, if one of the files has a problematic filename - either the name is too long or contains characters, that are not alphanumeric.
You can try to copy the the library in smaller blocks.
to open the Photos Library package and to copy the sub folder individually. Try to copy the library in parts. This way, you are able to identify the culprit that is causing the I/O error and can skip it, when copying: Be very careful not to modify the original library when you try this.
Create a new folder on your external drive. Call it "Photos Library Copy".
Ctrl-click (or right-click) your current Photos Library and use the command "Show Package Contents". This will open a folder, showing you the files and folders inside your Photos Library.
Copy these folders one-by-one to to the new folder on your external drive. If one of these folders is giving an error -36, check how far the copying proceeded. The files, that have been copied, are o.k. The file or folder, that should have been copied next will be the unreadable file. Probably the problem is caused by one of the files in "Masters" or a database folder. In that case look into the Masters folder and copy as much as you can, while leaving out the file that will not copy.
When you are done, rename the copy of your Photos Library to "Photos Library Copy.photoslibrary" and double click it to open it in Photos. Can Photos open this library?
The brand new drive is formatted OSX Extended Journaled
Is one of the drives perhaps formatted case-sensitive and the other not?