cPanel to cPanel server migration is an easy thing. But you need to taken care of small stuffs, otherwise it will screw up.

a) Check the old serve for the following settings

• Check mysql version
• Check apache version
• Check php version and apache+php configuration (  # /usr/local/cpanel/bin/rebuild_phpconf --current )
• Check for any third party modules like ffmpeg

b) Now you need to make the following  changes in new server,

• Upgrade/Downgrade mysql server to the same old server version
• Compile apache and php using easya apache and make it same as old server version
• Install and configure thirdparty modules same as old server

c) Set the name servers in new server ( 99% it will be same old )
d) Go to new server whm -> Copy Multiple accounts   , then give the old server ssh info. So you will get the list of  packages and cPanel accounts along with the size of the account
e) Copy all cPanel packages   to new server  , other wise you will get a lot of issues related with quota and packages
f) Copy small accounts ( size less than 2 )   via whm
g) Copy big accounts from shell  as follows ,
If you have a cPanel accuount named  "foo" which is more than 2 GB size  , then do the following

• # /scripts/pkgacct --skiphomedir  foo     ( This will take a backup of the account foo   without home dir , you can scp it to new server and restore it )
• # rsync -apvz --delete -s 'ss -p PORT' /home/foo  root@new.server.ip:/home/    ( This will sync  the home folder of old account with same permissions , make sure to run it on screen )

h)  If any account have dedicated IP and SSL make it so in new server
i)  Point the A record from old server to new server.