If you were asked what the time is, how would you reply?
"It's a quarter till three."
I never really understood the whole quarters fascination. It screws you over when it's x:30 or close. (Unless people say "half to 3...but I've never heard that.) And when I hear quarter to three, the first thing I do is mentally convert it to two forty-five anyway. Just more work.
The difference between 'to' and 'of' may be primarily American vs. British. The difference between 'quarter to three' and 'two forty-five' is, I'm convinced, mostly a matter of age. Listen to children and teenagers - they rarely use 'quarter to three'. Why? Because that is a visual reference to clock hands and they were brought up on digital.
It's quarter to three and two forty-five bouth same and right.