Hi there:
The snake/caduceus has a mohawk hair-do. The type used for Torrington is too severe- harsh. I would suggest a more 'graceful' font. Also I think the type should be a titling face as that was Eidict Neo- am I correct?- is more for text work. Also the sans (Gotham?) is blacker in appearance that Torrington which I'm not sure how that will play out in print.
As for which logo right now... the bottom one. As a person unfamiliar with the Torrington name/brand I would not grasp that the caduceus is representing the letter 'i' and not just a dividing element.
What are your colors for the design? Make sure the colors convey the feelings medical/science, natural, healing. I think you know I mean. Don't do everything in medical 'blue'.
All my best to you...
Mikey :-)