You just need the agreement from a supervisor in order to get accepted as a PhD candidate, and upon getting the agreement with him you are typically required to send CV, letter of motivation, and transcripts. Compared to other countries which use integrated application system such as US and Japan, I think the selection in these countries is more competitive. Students are required to take GRE in US and entrance exam in Japan, the questions in the latter case are even famous for its difficulty. So why do many people consider PhD selection in ETHZ competitive?
Could theoretically be slightly easier to get admitted for PhD than Masters, granted you have stellar recommendations & academic records and a professor who is happy to supervise you. Wouldn't generalize and say it's easier than MIT or TIT though. What course are you going for?
What makes a program competitive is the number of highly motivated high quality candidates with ideal background, that will be very good in the "job interview" too, and the expectations that come with it.
A general test is kinda useless to a professor that has to choose, if you have done a master in an excellent university it should say enough about you, or a master thesis in a group the professor knows. Some professors that have a lot of candidates may require you to know the complete research history of their group in detail before even considering you, that's a test if you want but pertinent, it also selects candidates based on their motivation not only intelligence.
European (especially mainland) PhDs are more like jobs than American PhDs. There is usually a big element in any PhD of getting in via contacts and references rather than standardised tests.
From what I gather the GRE isn't a particularly difficult test
By the way from some threads about PhD in ETHZ, I got the impression that most profs in ETHZ (and probably other Swiss unis) are rather bossy, can someone please give real examples, or your own experiences, how restricting they can be?
One more question, I would like to go back to the original matter, the competitiveness to get accepted in a PhD program in ETHZ. Someone has said above that, many consider it competitive because there are typically more than one applicants with matching criteria to the position. Well, since the application period is technically open all throughout the year, it may happen that one applies at certain time where there are no other applicants applying at around the same time. If this one applicant is considered ideal by the prof, he is technically accepted without any competition right?