An advantage of dialectical materialist thinking over mechanical materialist thinking is that dialectical materialism provides a way to understand the way things are related to other things necessarily, not simply accidentally. This is the essential technique which allowed Marx to advance beyond Ricardo in his analysis of value, where Ricardo got stuck due to his commitment to mechanical materialism.

The basic idea being that dialectical materialism constructs a totality of interconnected concepts which develops historically. The historical development implies a genetic relationship between concepts, which provides the dialectian with a direction when looking at empirical data. The mechanical materialist cannot help but get lost in the innumerable facts available empirically because they cannot integrate it properly into concepts, without introducing a form of eclecticism which destroys the basis of the concepts.

Edit: I wanted to add that in the end, dialectical materialist thinking is only a manner of thought which helps us reason about the world. A point of distinction between dialectical logic and mechanical materialist logic is in its interpretation of contradiction. The mechanical materialist assumes that a contradiction can only indicate a logical error or a wrong assumption. For Marx (as a great dialectician), a contradiction (can) indicate a point where the theory is too abstract and does not correspond to reality in some manner. Luckily in his reconstruction of Capital, humankind has generally already resolved the contradiction in practice - at which point empirical data is critically important. Rather than throw away the concept of value the moment a contradiction is found, he discovers how reality has dealt with the contradiction, and yet still he is able to keep a strong concept of value containing labor.

I think you'll be interested in Materialism and Empirio-Criticism. The benefits of the dialectical approach are in that it helps us understand relational phenomena, and prevents us from analyzing things as static and unrelational. A deer is not a deer without existing in the context that formed it and the trajectory it is going, there is no such thing as a deer in a vacuum. Dialectical materialism prevents us from thinking that way.

Okay, but you can study the way dialectical materialism makes falsifiable claims, because it claims to be predictive. Whether you feel like studying it or not is unrelated to the original claim.