How can I apply significance statistical test on my feature extraction method to prove better than standart one?

I have developed a new feature extraction method and I want to compare with the standard method. I extracted features from the same data. For this purpose, I used two different classifiers and found accuracy results for two different datasets. At this point, I couldn't understand how I can be sure my new method better than another one.

The dataset coming from the new method: M X N (M sample length, N feature vector length)

The dataset coming from standard one: M X K((M sample length, K feature vector length)

Obviously, the feature vector length is different. How can I prove my new method better than another by using statistical significance test? And which test should I use?