Dear prof. Parikh,
first of all, please check the convergence. If the solution converges for both methods and gives different results, please send us the model.

In most cases the full Newton-Raphson method, i.e., tangent predictor + updating the stiffness matrix in each iteration is the best/fastest. In some special cases, it may help to switch to the modified N-R method, i.e., elastic predictor + updating the matrix only once in each step.  See the ATENA Theory Manual for details, sections "4.2 Full Newton-Raphson Method" and "4.3 Modified Newton-Raphson Method".

Please see also the answer for "I get the warning "Convergence criteria (within line search) not satisfied due to eta limit, continuing superordinate iteration" during analysis, what does it mean?" at our ATENA Known Issues page, http://www.cervenka.cz/products/atena/known-problems