If you're happy that all your pictures are in iCloud, simply use a new, empty Library on the new Mac and designate it as the System Library. Then, provided you are logged in with the correct Apple ID, the iCloud contents will download into your new Library. This might take a long time depending on the size of the Library, but it worked very well for me.
It would be best if you select the option 'Download Originals to this Mac' as that seems to produce the most efficient handling, and sounds like that's what you have on your old Mac. iCloud will then keep everything synchronised, so your new Mac will exactly mirror the old. Disconnect the old one from iCloud before deleting anything, otherwise the deletion will synchronise across to the new one.
If you copy pictures from the old machine directly to the new, iCould will eventually sort out the duplicates, but it will duplicate everything first and will take forever. You do not need to ask how I know that!
Stephen