I just use a LiveDVD/USB (usually Ubuntu Mate, but it doesn’t matter) and DD the contents.
Example:
After swapping the drive in the machine with the new one, I put the old one in a USB caddy and connect it. Booting into the LiveDVD/USB, I check the mounts. In this example, I’ll use SDA as the new internal drive and SDD as the old drive in a caddy (use Gparted or df -h in terminal).
Next I make the copy in terminal with sudo dd if=/dev/sdd of=/dev/sda status=progress.
Once the magic is complete (will take a few hours) I jump into Gparted, resize the partitions to fit the larger drive, then reboot.