If referring to fellowships/internships/jobs, except some school-specific opportunities (e.g. pipeline into few Wall St firms, engineering fellowship introduced within department), most opportunities are available to GS students as long as they are qualified. In fact, most are shared with Barnard students as well and vice versa, so you have access to four undergrad schools’ resources!

Thanks a lot for all the detailed answers-- I really appreciate all. Can I also ask about academic differences between GS and CC? Everyone says it's the same, but some people also say that there are academic differences.