Hi OneblueTulip,
Only you can determine what the advantage for you specifically is.
In general, third party mail clients, such as Aqua Mail, offer greater customization and features in comparison to stock mail apps. Aqua Mail specifically is also an offline client - as in the e-mails in your account are only stored on your phone/tablet where the app is, and your mail provider's server.
If you have any specific questions we'd be happy to help you out!
Martin