Since the two drives are different capacities it's best to create a hard disk image of the 1TB drive, then restore that image to the 2TB drive, remembering to tick the option to "proportionally resize" the image when restoring it so that it fills the entire 2TB of the drive. If you fail to tick that option, you'll end up with a 2TB drive which has only a 1TB partition on it.
You can achieve all the above by using Active@ Disk Image: http://disk-image.com/
Don't forget to create a boot CD containing a bootable version of Active Disk Image. This allows you to access the disk image file for restoring to the same or a different hard drive. The program contains a Windows utility for creating a bootable CD. Creating disk images can be done from within Windows (and it does work) or you can create one from the bootable CD version of the program if you prefer.
There are other disk imaging applications, some of which are free, but I can only recommend the one that I have used for several years with no problems whatsoever.