If you legit have an offer from a different company take it.
No way. You might walk through the door at the other company, realise it's a horrible place to work, and hand in your resignation at lunch time.
Take the pay rise. If they fire you a month later, you'll at least get a big severance package to cover your living expenses while you look for a new job. If you quit, then quit again, you're going to be delivering pizza's or something while you look for a decent paying job.