Are copies using rsync faster than using Finder?
You didn't do wrong, but the point with rsync is that after the initial backup/copy, subsequent rsync runs are clever enough to only copy/backup stuff that's changed. So say you do your 300GB backup, then a week later want to backup again, if you've only made 5GB of changes on your disk, then rsync will only try to edit/backup this 5GB, rather than you having to copy over the full 300GB again. This is the time saving you benefit from when using rsync, and you only get it when you're running regular backups of the same disk. 

So the answer to your question is no, for a one off copy operation, rsync and finder are likely to be exactly the same - indeed, it may be the case that finder is slightly faster. Rsync is for keeping/maintaining an up-to-date backup of a working disk, and the time savings are in the long-run, not taking the initial backup.  

To get the benefits from rsync, you should take a copy of your rsync command, and store it in a way you can run it again at some time in the future (for example, you might embed it in a batch/script file that you can run periodically in the future). The next time you run the same backup, it might take 5 minutes, since it's unlikely that you will have changed that much on your disk. 

So for example, here's the content of the script file I use to keep an up-to-date backup of my music folder on my mac - this is set to run every 24 hours:

#!/bin/bash
rsync -ariv /Users/myuser/Music /Volumes/data/media/myuser


The first time I ran this it took ages too, but now, when I run it again, it just backs up what's changed in my Music folder, and might take a minute or two. Meanwhile, I know that I've got a 100% up-to-date copy of my music folder in my backup drive that I can go to should my primary drive fail.