The accurate and quick derivation of the distribution of damaged building must be considered essential for the emergency response. With the success of deep learning, there is an increasing interest to apply it for earthquake-induced building damage mapping, and its performance has not been compared with conventional methods in detecting building damage after the earthquake. In the present study, the performance of grey-level co-occurrence matrix texture and convolutional neural network (CNN) features were comparatively evaluated with the random forest classifier. Pre- and post-event very high-resolution (VHR) remote sensing imagery were considered to identify collapsed buildings after the 2010 Haiti earthquake. Overall accuracy (OA), allocation disagreement (AD), quantity disagreement (QD), Kappa, user accuracy (UA), and producer accuracy (PA) were used as the evaluation metrics. The results showed that the CNN feature with random forest method had the best performance, achieving an OA of 87.6% and a total disagreement of 12.4%. CNNs have the potential to extract deep features for identifying collapsed buildings compared to the texture feature with random forest method by increasing Kappa from 61.7% to 69.5% and reducing the total disagreement from 16.6% to 14.1%. The accuracy for identifying buildings was improved by combining CNN features with random forest compared with the CNN approach. OA increased from 85.9% to 87.6%, and the total disagreement reduced from 14.1% to 12.4%. The results indicate that the learnt CNN features can outperform texture features for identifying collapsed buildings using VHR remotely sensed space imagery.