I'm just catching up on research here, and when I see a new study that the world's foremost researcher on back issues Stuart McGill is involved in I pay attention.
In the latest issue of The Journal of Strength and Conditioning Research (23(2)/350-358) said study compares three different rowing exercises and stresses upon different areas of the back. Specifically they looked to quantify muscle activation of the spine and hip extensors, spinal loading, and muscle stiffness.
The three movements are an inverted row, a single arm cable row, and the standing bent-over barbell row.
Previous studies have shown that muscle stiffness (in other words how stable the spine is) is a good way to determine back health and/or injury risk.
Not surprisingly the bent-over row had significantly higher spinal compressive forces than the other two movements - something everyone should consider in exercise choice, especially if there is a history of back troubles. However due to the spinal loading and demands on the core musculature the authors recommended this lift for athletic training for the purposes of preparing athletes for the compressive forces generated in many sports.
The inverted row had the least amount of compression but the highest amount of activation of the thoracic and upper back (where most people are weak).
Applying these results to the general population one can say that for most people a reasonable progression would be from one arm rows to inverted rows, and finally if core and spinal stability levels are sufficient and nedd is present, then to bent-over rows.