this will depend on the goals of the move and the architure of the systems in question. There is not much context here to go on however it mught make sense to test for the performance post the move is at least no worse then current. It may also be worth checking on the security of the system on the new servers, ie is the access the same, can other DBA's bring these boxes down?
In fact there are many additional non functional aspects that may be reasonable to test for: recoverablity of the new servers, if they are covered by any exisiting Disaster Recovery process, are the "operational monitoring" activities in place on these new boxes, do these new boxes have enough disk space to allow for datagrowth, are these boxes designed to co-host other apps/ databases and does this affect functionality or other systems characteristics that have an importance to the business?
Agile Testers of the World UNIT!
In addition to what Neill has said, remember that sometimes you run into tables that are shared by multiple applications, so that whey you move such tables to another platform there can be a ripple effect. You should definitely not limit testing to what you are moving, you should also do some sanity checking on what stays on the other system to make sure nothing was compromised accidentally.