Had a similar situation about a year and a half ago (although not at a management level). I had a boss I didn't really like working for and we had a couple of dust ups. Nothing bad, (he probably didn't even realize they were dust ups) but he basically said a few things to me that made me think I didn't have a lot of support going forward. I also knew that I could make a lot more money elsewhere and that they were basically dangling a promotion I'd already earned in front of me like a carrot so that I'd keep pushing hard through the end of the year (I had basically made my sales goal by May)
So on a whim, I applied for an open position at a competitor. It was actually the company where I'd started my career (left on good terms the first time due to a regional restructuring). They called me within 2 days of posting for the job, and I was out there for an interview within a week. They offered me a job less than 48 hours after that with what ended up being like a 30% pay increase.
Went to my boss (and his boss, who I liked) and laid out the situation for them. I expressed my frustrations with the situation and basically told them I wanted to stay but needed some assurance that I'd be taken care of going forward (in terms of promotions, training opportunities, etc). While they were able to give me a little bit of a bump (like 1/3 of the difference) it was still way below the offer. And to be honest, I was concerned that they'd give me that raise but then basically hold it against me when I (hopefully) got the promotion at the end of the year. (giving me a token additional bump)
After a night of soul searching and basically trying to find a reason to stay, I decided I really couldn't. One of the tipping points came after talking to my uncle, who is the CEO of a rather large company in my industry. He basically told that from a management perspective, if I stayed, I'd likely always been seen as someone who is just looking for every dime I could get. My concerns about management style and the way I was treated would be totally ignored because, in their mind, I was just some guy who would jump at the next chance to make an additional 10%.
So I guess what I'm saying is...if you're going to bring the offer to them, you better be damn willing to walk. Despite the extra money, I regret my decision every day. Ended up with a good company (large corporation) but my particular department has systems, workflows and strategies that I just can't stand. Basically making myself miserable for an extra few hundred bucks a paycheck. Not even close to worth it.