I would install the minimal system on the new computer and then copy the _list_ of installed package on box1 to box2.
As soon as you have the list, you ask box2 to reinstall them (probably it will redownload them)
On box1
Code:
apt-get update
apt-get upgrade
dpkg --get-selections > /tmp/box1_list
On box2
Install a base debian system
Code:
apt-get update
apt-get upgrade
cat box1_list | dpkg --get-selections -
apt-get dselect-upgrade