is there anything like $view_mode in user-profile.tpl.php
I don't believe there is. There should be, and if I had to guess I'd say there will be in D8. Large parts of the entity api simply didn't get implemented in D7, and nodes were probably just considered a higher priority.

I believe the Profile2 modules work by extending the user entity, it may provide you with what you want.
Otherwise my suggestion is Panels, which can control the user view via something called "Selection rules", instead of view modes.