Different websites will have different many different factors, including how they calculate their final numbers, such is the problem with any scientific data. For your diet, though, don't worry about it too much. If your diet is so strict that the minor differences in nutrition facts make that much of a difference, then will you have the energy to stick with it in the long term?
Every egg is different, so the chances of the one you eat exactly matching either of those sites is nil. Not to mention that the accuracy of those numbers depends on you measuring ingredients with equal accuracy.
Use the database to learn quick estimates for the foods you commonly eat, so you can make decisions without the computer nearby. If you are out eating, knowing that an egg has about 75 calories and 5 grams of fat, for example, lets you decide how many you want.
Edit:
If you are looking for another database, though, the search at Wolfram Alpha has many foods. Try typing something like "bread nutrition."