Which of these designs is better? What are the pros and cons of each? Which one would you use? Any other suggestions of how to deal with methods like is are appreciated.

It is reasonable to assume that Draw() is the only place that the other draw methods are called from. This needs to expand to many more Draw* methods and Show* properties, not just the three shown here.

public void Draw()
{
    if (ShowAxis)
    {
        DrawAxis();
    }

    if (ShowLegend)
    {
        DrawLegend();
    }

    if (ShowPoints && Points.Count > 0)
    {
        DrawPoints();
    }
}

private void DrawAxis()
{
    // Draw things.
}

private void DrawLegend()
{
    // Draw things.
}

private void DrawPoints()
{
    // Draw things.
}

Or

public void Draw()
{
    DrawAxis();
    DrawLegend();
    DrawPoints();
}

private void DrawAxis()
{
    if (!ShowAxis)
    {
        return;
    }

    // Draw things.
}

private void DrawLegend()
{
    if (!ShowLegend)
    {
        return;
    }

    // Draw things.
}

private void DrawPoints()
{
    if (!ShowPoints ||  Points.Count <= 0))
    {
        return;
    }

    // Draw things.
}