I actually found Blair Witch compelling. The FF shots don't really bother me.

Cloverfield I saw on the big screen. My buddy walked out about 10 mins in... he got sick on the shaky camera work. Actually, the minute after he left, the rest of the film toned down the shaky shots a lot. The last half the of film was technically FF, but it was more like a normal-shot film as they got very creative to tone down the FF limitations.

Personally, I don't think the FF ruined Cloverfield because I enjoyed the novelty of the POV as a story device. I mean, I've seen giant monster films, and the general film elements of Cloverfield: story, characters, etc, were not
great by any means, so the special perspective view was a cool experience to me. I think the big screen enhanced that too.

The original Blair Witch was a trailblazer, but it didn't age well. Some movies don't.