I'm not sure if "style" is the right word, as it implies the medal was originally worn for stylistic purposes rather than for service.
One misconception that people often make is that the USSR and Russian Federation are two completely separate, distinct entities. This isn't entirely true. The Russian military remained relatively structurally untouched by the transition, and many people in positions of power started their climb during the Soviet era. Certain awards, including the Hero of the Soviet Union (although I don't know if this is the case past the early 2000s), are eligible for wear by modern Russian personnel, although people old enough to have been awarded the HSU that are still "in" are few and far between.
In addition, the HSU title lives on as "Hero of the Russian Federation," "Hero of Ukraine," "Hero of Belarus," and so on. The medals are stylistically similar; the only difference is the ribbon (in each case, it's one of the respective national flag) and the text on the back. Though I cannot speak for Belarussian uniforms, HRF and HU medals are worn the same way as the HSU. The criteria for receiving it remains more or less the same as well.
In short, the Hero of the Soviet Union hasn't really gone anywhere; it's just had a new coat of paint on.