The rapid growth of technology has initiated the development of automated system in various fields, including medical. One of the application is an automatic bone assessment from left-hand X-ray images which helps radiologist and pediatrician to take a decision regarding children's growth status. However, one of the major issues in developing this automated system is determining the appropriate technique which can produce effective and reliable prediction, especially when dealing with vast amount of data. The dataset used in this work is taken from RSNA bone age dataset which has 9 GB size consists of 12.611 images with various resolutions. To overcome this problem, we implemented and analyzed two different approaches for automatic bone assessment: deep learning and classic machine learning. For the deep learning approach, we utilized two different pre-trained Convolutional Neural Network (CNN) models, i.e. VGG16 and MobileNets. On the other hand, classic machine learning approach implemented Canny edge detection to extract image feature and several traditional regressor algorithms. Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Symmetric Mean Absolute Percentage Error (SMAPE), and time execution are employed as evaluation metrics. The results of our experiments show that deep learning based VGG16 model performs better in predicting bone age values compared to classic machine learning. The MAE and RMSE achieved by VGG16 are 14.78 months and 18.93 months respectively. However, classic machine learning approach has better error percentage in general, marked by lower SMAPE, i.e 28.34%. In terms of time execution, classic machine learning approach performs 10 times faster than deep learning based approach.