When I think of deep edges, I would usually look in the step sequences and transitional edge work before the jump landings or two-foot highlight moves such as spread eagles, although those can also certainly show deep edges.
Aside from the depth of the lean, I would also consider speed and acceleration, flow (maintaining an even glide rather than continuously losing and regaining speed), and the security of the edge (no wobbles).
Agility (ability to change directions quickly and efficiently) is also valuable, but not directly related to the depth of the edges and sometimes works against it. Maintaining or gaining speed through multiple turns and steps is certainly an indication of good edge skills.
It seems we tend to see more quick steps and changes from smaller skaters and longer-held edges from larger skaters: think Orser vs. Boitano.
For the Shin Amano fans, here he is competing ~20 years ago:
https://www.youtube.com/watch?v=BxsLy2xFSEY
https://www.youtube.com/watch?v=YXGfaDBtNuw
please a loose one with curly hair. He could stylishly lose it during the SP steps!
Touching his hair with my profane hands... those fantasies would derail not just one thread! 
