There is no real difference. Both nlinfit and fitnlm are Statistics Toolbox functions for nonlinear regression, and so use the same fundamental functions. The fitnlm function is a shell around nlinfit and its friends. The advantage to fitnlm is that it’s slightly easier to use, and delivers a few more statistics. The important results — parameter confidence intervals and confidence intervals on the fitted equation — are easy to get with either, but actually slightly easier with nlinfit, nlparci and nlpredci.
Experiment with both, and see which is most appropriate to your application.
Don’t neglect lsqcurvefit if you have access to it (Optimization Toolbox). It can do two things that the Statistics Toolbox functions cannot: (1) accept bounds on the parameters, and (2) fit matrix dependent variables. It doesn’t have access to all the statistics the Statistics Toolbox functions do, but it definitely has its uses.
