Top Secret Clearance with possible dual citizenship with Russia

Is there a difference in obtaining the clearance?

State department does their own investigation and it is easier to track your progress.

Take a look Guidelines B and C within Security Executive Agent Directive 4 (SEAD4). This should give you more guidance on the dual citizenship issue. Although I’m not sure who’s really following this directive, it eases the burden of foreign passports and dual-citizenship depending on the circumstances though.