I think it's actually the round nose with flat meplat at the tip that's a more traditional shape for tubular magazine loading. There were conical bullets (sharp point) for revolvers, like Webley made, but I think the truncated cone is popular, as Nick said, for speed loading. Webley may have had the same idea about ease of loading under stress. Jeff Cooper also held, based on field reports, that it was a better stopper in .45 Auto than round nose hardball.
As to ballistics, the sharper point will have a higher ballistic coefficient than a wadcutter. For that reason, if the velocities match, it gets to a 50 yard bull's eye target a little quicker and with a little less drop or drift. Otherwise, I don't see a reason to prefer one over the other. The wadcutters, as their name implies, are made to cut clean holes in paper for scoring, which they do. The double-ended wadcutter has the theoretical advantage that its geometric center and center of gravity are co-located so that any bullet tilt in the barrel should not move the CG off center, as it does in other shapes. Off center CG produce drift, but pistol ranges are short enough that you don't normally have big errors from this anyway.