I don't fly the 737, but Level Change and VS are Level Change and VS. When near the ground (less than 5000ft AGL) be wary of quite steep descent angles if using Level Change and say Speedbrakes (or other drag creators). I have seen some VERY steep angles resulting in very high rates of descent, all because George (the A/P) is chasing the speed with the nose attitude.
VS is much neater, as it allows YOU to control the rate of descent (as mentioned by Denti your company may even have descent rate rules down low) to a manageable level. In VS, if you get too slow, the A/T will kick in to keep it where you want it. IMO, it's better being under control sinkrate-wise and using power than the nose going down and down and down at idle as the jet tries to chase the speed.