The UT Austin FAQ section is very informative:
They mention that: "Due to the high volume of requests and applicants (approximately 500 a year) we cannot provide you with an estimate of your chances for admission. Admission is highly competitive and is more so for International students due to the higher volume of applicants and fewer admits. For Fall 2006 admission we had approximately 287 Foreign applicants and only accepted 23 for admission. For US applicants there were approximately 183 applicants and 60 were admitted. A total of 83 were admitted with 32 new students enrolling, 11 International and 21 U.S. students."
So it is evident that competition is much stronger among international students. I would assume these stats to be comparable at other well-known institutions.
For people asking about when they will hear from the programs they are applying: "Our Graduate Recruitment Committee will begin to review applications in late January. Decisions should take place in mid February for US applicants and early March for International applicants."
This should definitely vary among institutions.
Finally, they are not as hermetic regarding the GRE averages:
Int'l U.S. ALL
Verbal 510 605 574
Quantitative 788 782 784
Physics Subject Test 908 760 806
As you can see, the difference between the GRE scores of domestic and international students is pretty huge.
Hope this helps.