I work in health care and I've been lucky enough to get an offer from a competing company. Although I like my current job, it's a pretty generous offer. Should I tell my boss and see if my current company will make a counter-offer, or just accept the offer and leave?
Congratulations on getting a competing job offer -- that's not easy to do in today's workplace. As for what to do with it, well, this is a situation that needs to be managed carefully. If you do talk to your boss and get a counter-offer and ultimately decide to stay, you don't want to create the perception that you're disloyal and just out for yourself. And if after discussing it with your boss, you still decide to leave, then you want to do so in a way that leaves open the possibility for you to one day return.
Keep in mind that trying to get your current company to make a counter-offer is generally a strategy you can only use once. If you use it again, you'll be seen as someone who's continually seeking out other opportunities to gain leverage with your company, even if it's not true, and chances are you won't get another counter-offer. So what you've been offered now should be substantially better than your current situation in order to make it worth your while.
If you do decide to bring this up with your boss, be careful to frame the offer as an opportunity that just came your way and not one you actively sought out. And don't belie that assertion by revealing too many details about the offer, since that would show you've already walked down the road some with your company's competitor. You might then say the offer is something you feel you had to consider, but that you feel loyal enough to your current company to want to talk it over. What you tell your boss about how the offer came about and how you responded will all be part of his or her calculation of whether to make you a counter-offer.
For an example of how not to handle this situation, consider what happened to a manager on the rise I once knew at a consumer products company. When he discussed the offer he'd gotten with his boss, he shared not only what the salary offer was but that the other company was offering to find his wife a job and help them both find housing, as well as several other perks they had dangled in front of him. This implied that he'd already had fairly extensive discussions with them, and his boss declined to counter and essentially let him walk.
By contrast, one of my clients at a manufacturing company was in the same situation a few years back, and told his boss about this great offer he'd gotten that he felt compelled to consider. His boss understood and knew he couldn't match it, so my client was able to leave on good terms. Several years later, he decided to apply for a higher-level position at his old company and he was welcomed back. And that's the way to handle it so that the situation is all upside for you.