Is this true? Is it better to use Mail.app than using webmail?
In practice no Mail.app is not more secure.
The reason being that most mail providers also provide a webmail service e.g. Gmail, iCloud, Outlook.
So you have the risks of webmail as well as possibly other from Apple Mail. the attacks against Apple Mail are different.
Now if you could find a mail provider that does not provide webmail access then there might be something in the original premise. However there will be other security issues and so you can't say one is more secure than the other.
Remember security is relative. Nothing is 100% secure. You just have to choose how secure you need it to me. A CIA operative will have different needs to a normal member of the public.