> tell your current employer about the offer you've been made ... and see if they counter offer.
That seems like it would come off as worse than taking the new job. If I was OP's current company I'd see that as 'not only did you shop around first couple weeks here, but you're now rubbing it in our faces and expecting us to reward you.'
"Listen, I really like working here, I like that you guys do x,y,z, that I have the option to learn from/about/with.. whatever, but I've just had a great offer from Acme company, and I was going to take it, but wanted to talk to you guys about it before I accept."
That way the company understands why the person is leaving, that they haven't agreed to leave yet, it is in the employers hands to keep the employee if they want to.
We have a fairly small industry (and even if we didn't) you're going to be running into the same people again and again though your career. Neither side should be hurt in this. It's a business proposition. Friendships don't have to end, cooperation doesn't even have to end. MAKE SURE YOU ARE NOT LEAVING YOUR CURRENT EMPLOYER IN THE LURCH. Give them time for you to clean-up what you're working on and get it in a good state, etc. etc.
As long as you're professional (and the OP's original posts suggests he is professional and courteous), the current employer shouldn't take it as anything but.
And no matter what your approach, some bosses will take it one way, others another way! And that's OK, do what's right for you, don't make your choice based on whether you get a cold reception or not.
It's just business. Everyone knows that the quality employees almost always already have jobs - chances are good that your company also will poach candidates similarly.