Match an image from a set of images : Combine traditional Computer vision + Deep Learning/CNN
In my opinion, if you want a hybrid of Convolutional Neural Networks and the classic feature extraction techniques that would be redundant. Mainly because the architecture of a Convolutional Neural Network is composed of convolutions. I won't go much into detail of the whole architecture but these convolutions actually extract the good features for you and then those convolutions are connected to a classic Neural Network that does the classification task. Hence, extracting features using SIFT and using Convolutional Neural Networks would be redundant. In addition, the features that CNN will extract are better as compared to simple SIFT features. Though if you want to push through with combining SIFT and Deep Learning, you can instead substitute convolutions and use SIFT for feature extraction and then feed it into a Neural Network. That would work as well.