Need precise description of what you did the two ways that you think are more different than what you expected. I've got the curve fitting toolbox but haven't yet had time to explore with it. But I'd certainly think if you enter the same model manually as the auto one and use consistent data and fitting techniques the results should be essentially the same.
IOW I think you've done something different to cause the difference whether you recognize what that something is or not.
You can apparently (as I read the documentation, anyway) add constraints on any of the parameters of the chosen model in the options dialog. I see it also says it only uses the constrains with the trust region fitting algorithm.
