Best method of capturing computer screen. Software versus external recorder.

Hello.

I am working on a training video project in Premiere and After Effects.

I need to capture a lot of screens from an online application while the user navigates and narrates.

In the past I have used ScreenFlow from Telestream to do this. It has been fine.

I have heard that one might get better results using an external video recorder via the HDMI connection.

I have a friend suggesting Convergent Design's Odyssey 7Q+

Doe anyone have any thoughts or insight into which approach is best?

The final project will be used online, in classrooms and in conference presentations.

Many thanks.

A.S.