I have noticed two types of 3913. There's the one that looks like every other S&W semi-auto, and then there's the one that has a taper, running from the trigger guard to the muzzle. Is the one with the taper, the original Lady Smith, that later became the non-ladysmith? Is one better than the other, or is it just a matter of preference?

It's all a matter of preferance, although I've heard the one like the ladysmith are a little hard to find holsters for.

Yes they are the same exact pistol but with a slightly curved frame and the NL/LS have a single sided safety. I own both models and find no real difference in the 2. As JumpinJack mentioned, the LS/NL pistols are a pain to get leather for. Most of the time they will not fit a regular 3913 holster.

Leather may be a little more rare for the tapered frame, but I have seen all the big name holster makers with the 3913 LS in their lineup.

Not saying this always works, but my LS fits perfectly in several holsters I had for a 669, including my old favorite Don Hume.