Start with mathematical equations. Both techniques have their own equation. In terms of SIFT, the result varies due the values of sigma. You can calculate HOG to determine The sigma values dynamically.

A simple start would be concatenating the features and train a linear classifier with them. The idea here is to compare whether this classifier achieves better performance than when it is trained with only or SIFT or HOG. Usually, the concatenation approach will produce better results.

To get the best of both features, one can use a feature selection strategy. The simplest way to do it is by employing a score that indicates how well a particular combination of features works. Here one can start with Fisher score, although other options exist.

I recommended you to take a look at the deep learning models they are powerful features extractors that outperform the classic descriptors like SIFT and HOG.

Upto my knowledge you cann't combine these two. But using image registration techniques you can match HOG features with HOG and SIFT feature with SIFT for the same image. This kind of approach probably increase your classification accuracy.

I am with Dr. Dairi Abdelkader opinion.

Thanks every one for your valuable opinion.

@Dairi Abdelkader sir i completely agree with you CNN can capture far more abstractions of the features and thus can outperform those conventional machine learning technique.