I've used a program called CopyWipe to move everything from one HDD to
another. It automatically deals with the partitions and everything. I've
tested several of these types of programs and this was the best.

I'm not sure how well it works with Linux. I think I tried it once, but
can't remember.

http://www.terabyteunlimited.com/copywipe.php

See attached link:

http://clonezilla.org/

This is a live cd for linux which enables you to back or copy complete
partitions or hard drives. It is for linux and I have used it to do just
what you want to do - it works well

I don't know how to do this under Linux, but in Windows it would be as follows.
If you have the utilities CD that came with the new drive, you can use that to
clone the small drive to the big drive and use the big drive as your master.
Set both drive jumpers to cable select (CS). Install the new drive as the
slave, preferably on a different cable from the old drive, like with the CD/DVD
drive. Put the CD in the CD drive and boot the machine. Follow the directions
and the CD will lead you through the process. Take your time, be careful, and
follow the directions.

I've found the most efficient way of saving data and allowing for
linux upgrades is to use a remote hard drive - all that remains on the
m,ain hard drive is the operating system. 6 month upgrades are fine if
you do this...

On my Windows box, I use a smaller drive for the OS and software and I use a
large drive for the data. You could do that on your Linux computer. Just
leave your software on your small drive and use your new drive as a slave.