Which would you rather work for? Don’t stay just because of habit, but, otoh, if all your issues are addressed, and it would genuinely be better to stay, and you’ve worked out why they didn’t pay you enough before, then consider it.
But remember it looks like you don’t get a raise without asking.
The “new salary on the other company’s letterhead” thing is complete bull. It’s not standard practice anywhere, and can only serve to make you look less serious to the prospective new employer. the absurd claim that it’s a “HR requirement” can easily be countered by saying that you have your own requirements, and the (old) company isn’t meeting them.
I once took the bait of a ridiculous counteroffer and it ranks with the worst mistakes I ever made in my life (A promised raise never materialized, the other job offer disappeared, and a year later I was fired without cause). From what you’ve described, there is no good reason to stay at your current job.
Don’t do it.
It’s HR being a bunch of morons. If it were me, I’d also tell them to stop being ridiculous too.
If they want to keep you, they will make you an offer you can’t refuse, and not demand proof.
IOW: fuck 'em.
The new employer is living in the real world. The old place doesn’t seem to have a clue. You want more pay and a more enlightened environment. Thank them for the time you’ve spent with them and move on. Fourteen bucks an hour doesn’t put you in the driver’s seat at the old place anyway. Good luck and happy NEW JOB!!
I agree. Just say, “You’re the ones trying to keep me here. I don’t care if you don’t give me more money, because I’ve got an offer elsewhere that I’m happy with. I don’t need to give you anything.”
Just adding to the chorus of voices - don’t do it! If you’ve already told your “old” employer that you’ll reconsider, then go back and explain that you’ve slept on it and think you’re making the right decision by moving on. Don’t burn bridges, just be polite and stick to your guns.
It looks like you’ve got plenty of votes on the “don’t do it side,” but I’ll add mine anyway.
DON’T DO IT!!
For one thing, if you choose to go with the new employer, this will start you out on really bad footing. It could have a very negative effect on your integrity and your perceived loyalty.
Also, there is no way in hell that the HR department needs to receive something like that. That’s very unprofessional on their part to ask for such a document, and they should understand what sort of impact your asking for that would have on your position with your new company. And, realizing that your new company would probably frown upon you asking for something like that to leverage higher pay with your current company, your HR department is effectively asking you to sabotage your new position.
For the record, I have been told since high school that if I leave one job for another, never accept counteroffers from my old company. For one, they already know that you don’t have loyalty to their company, as you’ve sought a new position elsewhere, and another, if they were capable of recognizing your worth, they’d have raised you long ago, or done so simply upon your resignation. None of this “proof of income” hoo-hah. Accepting a counteroffer to stay with your previous employer is never a good career move.
Good luck, and enjoy your new position 
Peace,
~mixie
One more for don’t do it. A previous employer closed up shop to move to another state. I had a job offer and turned it down to move with said company after they presented a counter-offer. I moved with them and found out that the “raise” was the lack of state taxes in NV, the promised position was filled before we even left California, and I was stuck with them for at least a year or I had to repay my moving expenses.
The previous isn’t a rant, it’s to let you know (worst case) what counter-offers can turn out like.
It sounds like your company is the type that would pull something like that. Get out and good luck in the new position
Peace-DESK
Oh yes, a major point that Igloorex made and shouldn’t be overlooked.
If you stay and they give you this raise, you can forget about getting annual raises for a while, because “we just gave you one”.
Yeah. Don’t do it. Your old employer now knows that you’re unhappy and are open to new offers. Also, your new salary is more than they could pay someone else (after all, they got you to work for the lower figure, right?). So…it’s a very short step to finding a way to get rid of you down the road. Perhaps they can train (or, even worse, have you train) a replacement. Then you’re dispensible.
The chorus is deafening: DON’T DO IT.
A happy tale: Four months ago, I left a job at a company I liked because I felt my boss was deliberately holding me back. Crappy raises, promotion “maybe next year”, etc. I found another, similar, job elsewhere. Two weeks ago, my old employers called. My former boss had been fired and they wanted me to come back with a promotion. All the money I’d previously been asking for and then some. Did I take the offer? Sure.
So, rostfrei, are you going to tell us what you did (or didn’t do) in the end?