By mentioning local do you mean the bundled MS SQL server express edition? If so, it depends on the size of your infrastructure.
With the SQL Server Express edition database, vCenter can support up to 5 VMware ESX hosts and 50 virtual machines in the inventory. If your environment is bigger than that or there are chances to get this scaled up in near future then I would suggest to go for an enterprise database software which are supported by vCenter Server. Eg: Oracle, MS SQL server (standard, enterprise, datacenter), IBM DB2
vCenter server and database server (except bundled SQL server express) are installed on the same Physial server or a VM are not recommended.
Its good to keep the database on a seperate VM/Physical server for better administration, backup and to avoid failures.
Please refer the following best practise guide . Section 5.8 for Database guidelines.
http://www.vmware.com/files/pdf/techpaper/vsp_41_perf_VC_Best_Practices.pdf
We can see the compatible databases to each vCenter releases in VMware Compatibility matrix.
http://www.vmware.com/resources/compatibility/sim/interop_matrix.php