Which of these two is the proper way to do a dumbell one arm row?

Yesterday at the Gym I noticed a few guys dipper far further with their dumbbell rows than me. I was taught to go parallel with the bench upwards and not from near the floor upwards.

So should the exercise be done this way:

or this way
 
I do them more like the second one, but I don't think it matters as long as you don't jerk the weights with your lower back and get a full range of motion.
 
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