With a big job like this, I would copy your drives' contents to the new one using Explorer/Finder, and take great care to replicate the same folder structure that you currently have.
Once that's done, take a backup of your LR catalogue, then right click the parent folders in Lightroom and choose update folder location. Point to the new location, and you should be done.
I'd do it this way not because of time, which would be roughly the same either way (maybe slower in LR), but more because of certainty. If you did it in LR and something went wrong during the moving process, it would be a lot messier to sort out. The above way means your existing setup will remain there until you're sure everything is in its new place.
John