Same chances for merit based awards. Except that since educational systems are differenent accross countries sometimes internationals do not qualify for fellowship ( i.e. they don't have required courses, gpa conversion problems etc.)
And I think international applicants might have slightly lower chances of getting TA/RA position due to the language problems.
And obviously internationals do not qualify for FAFSA, NSF and alike.
Other than that, I think internationals and domestics students have pretty much equal chances.