I think it depends on what your end-game is, and it sounds like this is a stepping stone for you.
If I was planning to keep the job for medium to long term, no doubt the King Air gig would offer better pay and benefits. But it won't do as much for furthering your credentials for a major airline, especially if you get stuck flying in the right seat for a long time.
If you're looking to use this as a temporary short-term position enroute to a better job, I agree with bedrock. While the pay and benefits are less, it sounds like you'd get the opportunity to get typed in the 737 which is a very valuable type rating. It's the best-selling airliner in history with over 8,000 delivered, many of those still flying, and with over 4,000 more orders on the books. And, the possible quick upgrade to Captain on it makes it even more valuable in terms of the experience it offers.
I'd say, if you're otherwise competitive for a major airline job (total hours, education, lack of negative factors, etc.), then go for the 737 job.
Good Luck!