Perhaps you should've put the old sprites on a separate picture to emphasize which sprite you want critique on. (I figured it was the rightmost sprite only, but clearly it wasn't all that evident.)
Paladin is right about pillow shading; it should be avoided at all costs. http://www.pixeljoint.com/pixelart/83718.htm
This is the only good example I could find, but generally, the thing that you should aim for to make it 'teddy-like' is to make the stitch lines noticeable, give it a round, soft outline all around (limbs, ears, torso) and cute, toy-like eyes. Your shading, especially on the ears, does not properly reflect the light source. Your colors are too desaturated, IMO, and you could probably drop a shade or two.
EDIT: What Gors said
Paladin is right about pillow shading; it should be avoided at all costs. http://www.pixeljoint.com/pixelart/83718.htm
This is the only good example I could find, but generally, the thing that you should aim for to make it 'teddy-like' is to make the stitch lines noticeable, give it a round, soft outline all around (limbs, ears, torso) and cute, toy-like eyes. Your shading, especially on the ears, does not properly reflect the light source. Your colors are too desaturated, IMO, and you could probably drop a shade or two.
EDIT: What Gors said