(For the record, I didn't vote on either questions)
Allow me to give a 'critique' of both questions:
For the first question:
First ten paragraphs explain a method to use Karnaugh maps to solve 3SAT. Then, 2 examples are given where this method works well and finally the question asks whether this method would work in general.
The question is a bit lengthy, but in general, it is on point.
For the second question:
The first ten paragraphs explain an interpretation of SAT and how to apply induction. This part could already lead some to down-vote, given that this 1. doesn't give any information about your question 2. anyone capable of answering this question knows about SAT and induction. Personally, I'd just scrap it or at least shorten it to one paragraph.
The rest of question explains the method and argues it could be efficient.
So, IMO, the first question is better, as it doesn't bore the reader in the first ten paragraphs by only explaining non-trivial background. Additionally, the examples are useful, as they show that the method may have some merit. Note that my critique is purely on the presentation of the question, which can always be improved. It is possible that the second question is also worse in content than the other, but I can't really evaluate that.
As for the reason why people vote, that's anyone's guess, as Raphael notes. But it could be the case that, as David Richerby states in this comment, that while most users are tolerant to a few questions about (most-likely incorrect) proofs about P vs NP, they don't like handling many of them. So, the down-votes could also be a discouragement to post similar question. However, this is just a guess. The only way to know is to ask the down/close-voters themselves.