I'm a character junkie, I think most people are. I prefer either close third limited or first person, and it doesn't matter which. For me, the level of tension is directly related to how much I care about a character, and most authors don't have what it takes to do that with omni.
Now, I have to say that my current WIP is in omni, but it also isn't a thriller, it's a much slower-paced book. I also have a pretty strong grasp of characterization, so I'm doing pretty well at a close omni. I just don't see that much in books. I think Neil Gaiman has done it well in a few, but he's in a league of his own and he doesn't do thriller.
It's hard to paint the emotionally charged scenes you need with the more distant POVs. I think that's why third limited distant and omni get chosen for the less dramatic books, or things where "feelings" aren't an issue. That, or they do well in a book like mine that has 7 MCs instead of one.