How to turn down a Postdoc scholarship offer that you already signed the contract for?
I am all but a hardliner when it comes to such topics, but signing a contract and then not taking the offer is a major breach of trust. This is not "close" to burning bridges. Unless the other side is the most understanding person in the world, this is going to go down really badly with the other side, and mark you forever as an utterly unreliable person, whose word cannot be trusted even after the paperwork is already filed. Frankly, if it is just about location and salary, I would strongly advise against changing your mind. The only time when this could be acceptable is when you get offered a faculty position instead of a postdoc.
After some more discussion, reading Pete's answer, and a good night's sleep, here are some additional clarifications to my answer:
Steve Jossup: "I wonder whether they're working on the assumption that in a typical contract the questioner has already contracted to work for the full duration of the scholarship without notice period"
No, that's not my assumption at all. I think it is perfectly ok to quit a two-year scholarship after one year, because something better has come up. However, to me there is a world of a difference between quitting after a year and effectively handing in your notice before your job even started. I do remember that there is a question here somewhere about what the shortest acceptable timeframe for quitting a postdoc is, but I can't find it currently.
Also, the comparison between postdocs and professional contractors is in this context quite helpful. I have been an software engineering contractor for a short time, and I would have never signed all the legalese paperwork for a customer and then immediately backed out because a better-paying customer came around. As a contractor, like a postdoc, you are living off of reputation, and this kind of thing is not good for it.
"Isn't there a chance that the other person would be ok with the OP cancelling the deal?"
Of course there is. Maybe the OP's original postdoc advisor does not care so much about this position anyway. Maybe the original postdoc advisor is really just that happy for the OP that he found a better post. However, in all the discussion so far, the OP has to the best of my knowledge never indicated that he plans on discussing with the other person. This question is all about telling the other person that he has changed his mind. There's an important difference.
Stephan Tarasov: "Why should it "could be acceptable is when you get offered a faculty position"?"
This is really just an amendment of the previous point. Even if you get offered a faculty position, you should not just tell the other person that you're out after all. You explain your situation to them carefully, and maybe they will understand and you will be able to renege without burning any bridges. The probability of the other person being understanding is much higher if the other post is objectively much better than the original one, which would be the case if comparing a tenure-track position and a postdoc position. A better-paying postdoc does not qualify.
Stephan Tarasov: "this should not hurt anyone!"
I am not sure why you would say that. The other person thought she is going to have an additional postdoc for a specified time frame, and now she isn't. How is that not very bad for her?
Stephan Tarasov: "Are you saying you keeping all of your promises all the time?"
I would say I try to. Anyway, a signed contract is certainly more than just a promise.
Anyway, I feel like I have said all there is to say on this matter. Still, I have created a chat room for this question, and should the OP or anybody else want to discuss this issue further, I invite you to discuss it in the chat room. As the commenting escalated a bit last night (surely my fault as well), I will not be answering any comments here directly anymore.