How to tell if you are on New Outlook or Classic Outlook is quite easy.
First the icons are different:
Here New is on the left (an envelope icon( and Classic on is on the right (envelope with letter, more square).
The toolbars are also quite different as show below.
New:
Has our logo and "Outlook" in the upper left. No user picture or initials in the upper right.
Classic:
Does not have our logo or "Outlook" in the upper left. Has your user picture or initials in the upper right.