I have WEBROOT SPY SWEEPER and NORTON 360 installed on my computer, I would
Like to know if both of them does the same thing as in protection. Is WEBROOT better
Than NORTON 360? Most important DO I NEED BOTH OF THEM to do the same thing?
Thank you in advance.

I don't believe you need both of them, though I've never used Webroot Spy Sweeper, and I don't really know that much about it. In general, however, having two "suites" of utilities doesn't work well -- they compete against each other and really slow down your machine.

If you want a second test, run an occasional manual scan with MalwareBytes Malwarebytes.org (http://www.malwarebytes.org)