If the new server is in the same AD domain:
it is not neccessary to install a new BESx, you could use the current.
setup the Exchange 2010 environment, so that it matches the needs for the BESx
(Configuring a Microsoft Exchange 2010 messaging environment - Installation and Configuration Guide - BlackBerry Enterprise Server for Microsoft Exchange - 5.0.2
move the besadmin mailbox to the Exchange 2010 Server
update the mapi profile for the BES
move one user to the Exchange 2010 Server, test.
then move the other users, either all, or some reasonable amout at at time.
If you want to install new BESx:
get a new BESx from RIM (free),
configure the current sql database to accept remote connections, and/or move the current SQL database to the new server: KB03112-How to move the BlackBerry Configuration Database to a new Microsoft SQL Server instance
Then, the old bes still should function.
Install the new BESx, and during the install point the installer to the correct database.
move the besadmin account to the new server
recreate the mapi profile on both BES
move one testuser using the BES console to the new server, test
move the other users
move the mailboxes for the users with the exchange console
delete the unused BES instances in the BES console
uninstall the old BES.
explained in detail here: KB12304-How to migrate the BlackBerry Enterprise Server to new hardware using a second SRP