Recognition of handwritten Bangla characters has drawn considerable attention recently. The Bangla language is rich with characters of various styles such as numerals, basic characters, and compound and modifier characters. The inherent variation in individual writing styles, along with the complex, cursive nature of characters, makes the recognition task more challenging. To compare the outcomes of handwritten Bangla character recognition, this study considers two different approaches. The first one is classifier-based, where a hybrid model of the feature extraction technique extracts the features and a multiclass support vector machine (SVM) performs the recognition. The second one is based on a convolution neural network (CNN). For recognition, we considered 10 Bangla numerals, 50 basic characters, and a subset of compound characters that are frequently used in the Bangla language. Experimental results demonstrate that the CNN model outperforms the traditional classifier-based approach, obtaining 98.04%, 99.68%, and 98.18% recognition accuracy for Bangla basic characters, numerals, and the subset of compound characters, respectively.