Perhaps open book/notes/web exams may be more realistic in terms of difficult problems in real life situations (including academic research). Closed book/notes/web exams may be best suited for simpler questions where it is expected that one would know the answer without looking anything up.
I remember one final exam where they gave a closed book/notes exam of simpler questions for the first hour. Then we turned in that paper and got an open book/notes exam of harder problems for the remaining two hours. (This was long before smart phones, tablets, web pages on every subject, etc…)