Linear vs Nonlinear method

Question

I am doing curve-fitting and I am trying to estimated four parameters. To solve the non-linear least squares curve-fitting problem I used the Levenberg-Marquardt curve-fitting method. To solve the curve-fitting problem in linear least squares sense I used the Singular Value decomposition (I used software to estimated the parameters). When my data are noise free both linear and non-linear least squares method seems to have the same accuracy. When I add noise to my data the linear least-squares method is more sensitive to noise than the non-linear method and I am interested to understand why this happen.