In the battle sometimes you need to maintain and improve the common crucial components to defend any attacks.
Let's compare it below:
Avast IS contains Hardened Mode, Sandbox, DeepScreen, and good core protection basis.
vs.
Norton Security Premium on the other hand has strong Cloud mechanism and active SONAR.
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In detection capabilities we can see that Avast is stronger than to Norton, considering that cloud functionality may be limited on other times.
However by default settings, Norton is better since the cloud and Sonar by itself is active and accurately prevent certain attacks whereas for Avast where Hardened Mode is off by default/moderate mode so the DeepScreen, CyberCapture and core protection may lead to bypass.
Avast Cloud Reputation is different in terms of effectiveness compare to typical Norton or even Kaspersky.
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Now in terms of customized settings then of course Avast is already in edge compare to Norton.
The thing I liked for Avast is sandbox component so at least you can browse in isolated safely.
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For ransomware or screenlockers, well both are in the mediocre stage and protection against possible alteration can be questionable.