Actually, when I first saw the question, I thought you were asking which school had the best application - as in which school had the best questions (short answer, essay, whatever) that would help them pick out the best applicants.
I haven't done any applications yet so I can't comment on their ease of use, etc., and to tell you the truth as long as they don't crash or have errors while I'm working on them I really don't care.
Before I read Rhyme's answer I was going to say HBS as well - for most comprehensive. You can tell from their questions exactly what they are looking for, and there is no way to hide. If you aren't exactly what they are looking for, it's going to stick out like a sore thumb. In fact, the more I look over their application, the more I feel like dropping them from my list. But even aside from my personal chances at HBS, I think their questions really go the extra mile to get distinguishing information from their applicants.
They are the only application that asks for tons of detailed information about each firm I've worked for - not just address and contact info, but also industry, function, size, annual revenue, etc.
They also ask for details about each extracurricular and go so far as to ask for contact information for each one. No other school has done this so far - most simply ask me to list, and provide hours, whether I was elected or appointed, etc.
It's by far the longest application as well - I cant remember all the stuff they asked now but it had a ton of information I had to look up. Then again, maybe it just feels that way because it was the first school I did - so virtually every question required some kind of follow up on my part ("Oh gosh, whats the annual revenue of that firm I worked for 4 years ago?" or "The phone number to that extracurricular? Geez, who the heck do I list for it?" or "What's my dad's official title at his job?") -- so maybe its perception - because virtually every darned field required some research or thought.
It's also the only school that asked me for six essays.