I have a problem with the omnibox in Chrome, the others are fine. In fact I expect to send my searches to another service when I use Google search and the default page in Mozilla Firefox. I wouldn't expect that every single thing I type in the url bar is sent to Google (omnibox case) and non technical people don't expect it either.

The expectation of privacy is the problem here. I don't find omnibox or the unity bar bad per se, I find it a privacy issue if the users don't clearly understand what is going to happen with what they write.