Fresh out of school I took the " a deal's a deal" route. Got an offer three days later for 13% more money, but declined based on the fact that I'd already accepted an offer from someone else.
Took my post-grad holiday, paid first and last month's rent on an apartment, moved in, and went to see my new boss. He said, "Hi, welcome to XXX- your pay's been cut by 5%". I'd rejected an offer 4% lower from them previously in negotiation.
Firm #2 had long ago moved on and hired someone else.
So there I was- rewarded for my "ethics" by 18% less pay than I could have been making, and 1% less than an offer I had already rejected.
Remember that this is just business and a job offer is just that- an offer. You can accept it- so you have an offer and acceptance. But since no money or other "compensation" changes hands, this does NOT CONSTITUTE A CONTRACT.
Work where you feel you'll do best- for them AND for you. Forget about which offer comes in first. Good luck to you!