Usually the company (which gave you an offer) would give you a couple of days for your consideration (up to one week), or you can ask them to give a period time for your consideration (don't ask for too long). You do not need to give them your excuses in this matter, or simply say for your family arrangement (e.g. spouse's job or children school). During the period, you must push hard to the other firm you prefer. However, you might need to make a tough decision at the final if no offer from the other before the period expires. Anyway, landing a job is better than no job, since (you may find out later) it is easy for one to get a job when one has a job. Good luck!
I think as long as you tell them the truth, they will understand. Anyway, you must make the final call since you are you own boss. Nobody could decide for you. Good luck!