Unless you feel you are in imminent danger of being fired from your current employer I would not take that offer.

You already know you don't think the new place is going to be much better.. but I think you are mistaken if you think an extra hundred or so after taxes each week is going to make you tolerate it any better.  More money seems to easlily become just status quo in our "reward center" part of the brain.. so very quickly.. all you will see is the downside of the pressur cooker.

Have you thought about changing fields?  It sounds like the jobs you are looking at are similar.. and if you keep doing what you have always done.. you will keep getting what you have always gotten.

Going into a new job with your mind mentally out the door is also not likely to be very helpful.  If you don't realistically see yourself in that job for a few years.. then I would stay in the leaking boat you have now vs going to the new leaking boat.. that you don't know whether their holes in the hull are bigger or not.  

At one time, I was working somewhere I was not happy.. my recruiter got me an interview with a company and they wanted to hire me badly.. at 10K more (this was 20 plus years ago.. so that was definitely more spending power then)  But, when I went for my 2nd interview, my potential manager's boss was a male organ.  He was all "you better not be afraid of hard work.. we don't plan our jobs for 40 hours a week.  You will probably work most saturdays.. and some sunday's too.  "Don't take this job if your Excel skills aren't high level"  Basically just being really aggressive.  I answered with all the right answers.. but when I got out of there. .I called my recruiter.. and told them that I was not working for that company.. because even though he would not be my direct senior manager.. crap trickles down hill.. and I was not interested in that kind of environment.. did I mention this job was literally walking distance from my apartment with a large, well known corporation with tons of potential for advancement? Yeah.. I was pretty devastated that this guy's attitude was so negative.. and my recruiter called me back.. pretty much said the manager really wanted me.. and would I please reconsider but I said.. "no"... if they don't make you feel comfortable going in the door... it was not the right move for me.  Within a month I was offered a job at another multinational level corporation at 24K more a year.. so.. sometimes things work out like that.. and I was with THAT company for several years before moving on. 

Lesson is.. don't be tempted to think just a little bit of money will make you hold your nose.. that will reflect in your work.. and you will be in no better position.  Wait for the right opportunity.. as long as you are not literally being FIRED.