Version 6 moved everything under PHPUnitFramework and left aliases for the old names, which are deprecated. Every test file extending PHPUnit_Framework_TestCase needs a line changing.
// before
class OrderTest extends PHPUnit_Framework_TestCase {}
// after
use PHPUnitFrameworkTestCase;
class OrderTest extends TestCase {}
The rename is mechanical and can be done with a find-and-replace, which is worth doing in one commit touching nothing else. The upgrade also drops PHP 5 support entirely and removes several assertion aliases — assertInternalType survives here and does not for much longer. Read the changelog rather than assuming the rename is the whole migration.