Tumor interface dynamics is a complex process determined by cell proliferation and invasion to neighboring tissues. Parameters extracted from the tumor interface fluctuations allow for the characterization of the particular growth model, which could be relevant for an appropriate diagnosis and the correspondent therapeutic strategy. Previous work, based on scaling analysis of the tumor interface, demonstrated that gliomas strictly behave as it is proposed by the Family-Vicsek ansatz, which corresponds to a proliferative-invasive growth model, while for meningiomas and acoustic schwannomas, a proliferative growth model is more suitable. In the present work, other morphological and dynamical descriptors are used as a complementary view, such as surface regularity, one-dimensional fluctuations represented as ordered series and bi-dimensional fluctuations of the tumor interface. These fluctuations were analyzed by Detrended Fluctuation Analysis to determine generalized fractal dimensions. Results indicate that tumor interface fractal dimension, local roughness exponent and surface regularity are parameters that discriminate between gliomas and meningiomas/schwannomas.