Sandi, It's a matter of how important you think the rosette. If the rosette completes a bloom, it will die. Pinching off the flower stalk can often result in the rosette producing another flower stalk whereas a vertical division results in two plants where "typically" only one plant may bloom. There are, of course, always exceptions. But offsets are not guaranteed. However, if you do vertical divisions, you can almost certainly end up with plants that will produce offsets, even if you have to repeat the surgery on a recalcitrant specimen.
Before I learned to do this type of division(back in the dark ages
), I had a large, very beautiful, single rosette that had been a no id rescue plant from a large store. the plant did beautifully after the rescue, going on to become very large and an unusual color. Over several years, I waited for it to produce offsets, but it never did. It bloomed a magnificent bloom stalk which I had removed several times. The boom stalk seemed to have hundreds of flowers on it, but in reality it was likely around 40, and grew to be about 18" tall. Of course, it fell over. But the plant never produced any offsets, not on the rosette or blooms stalks. It exhausted itself in producing flowers. That experience is what led me to experiment with other flowering (and non-flowering) rosettes to see if there might be a better way of preserving the plant.