At FIU, it's pretty much the same thing.
The SGA elections were held last week. The frontrunning team was composed of 2 Greeks, and their only competitors were a Greek/non-Greek. The school's newspaper went as far as endorsing the team with the non-Greek because of the argument that SGA and FIU is already ran by Greeks.
Needless to say, the ticket with the 2 Greeks won- they got about 61% of the vote. The Reps-At-Large, Housing Reps, even representatives for individual colleges like the College of Architecture and College of Business are ALL Greek. Which is pretty big, because SGA has about $10 million to allocate to student activities, organizations, etc.
The GDI population doesn't do that much at FIU. And luckily for us, the administration is very pro-Greek (our president, Modesto Maidique, is a SigEp).
Last fall, there was even an article in the newspaper by an incoming freshman complaining that at Freshmen Orientation, "the emphasis on joining Greek Life was higher than the emphasis on education" lol. (You can read it
here)
So I would say that Greeks at my school are pretty powerful.