The answer is No. Both applications have the same main functions: protection, security, optimization, but Windows Live OneCare has been discontinued by its developer and it is no longer supported. For this reason, I suggest you to keep HP Total Care Advisor and to uninstall Windows Live OneCare. You can remove it using Add or Remove Programs feature. Go to Start > Control Panel > Programs > Programs and Features, select the application and click on Uninstall.
After that, try running AdwCleaner to make sure that there are no leftover rogue registry keys or toolbars in your system.