If you compare, the old & new are diffrent in several ways. The imperial eagle is black. The republic is gold. The collar of St Andrew is gone as are the escutcheons- small shields are also gone. The other symbols are universal heraldic devices, representing, justice, unity and authority.
As GD Ally mentioned, many countries use old, or modified heraldic arms, even though they have long since shedded a monarchy. This provides a viable link with the country's history and a sense of continuity. The Soviet Union created a whole new set of arms, not to obliterate the past, which is an impossible task and a mistake, but to symbolise a totally new system. Although many of those symbols remain, on buildings and such, it is not out of fondness for the USSR so much, as it is too difficult to remove them, carved in stone as they are, so to speak.
