First of all let's figure out why construction estimates may differ so much.
Supply and demand.
If at a given moment a company has more customers than it can handle, it will raise the prices to eliminate less profitable leads. And vice versa when a contractor is too desperate for work he will start cutting down prices, as well as corners to keep the project at a profitable level.
Contractors use different approaches. For example: you have a water stain on the ceiling, you want the issue fixed. One person comes up at a lower price, as he deems surface is not so badly damaged and merely applying stain blocker and a coat of paint should be the best solution moneywise. The other guy considers replacing the whole sheet of drywall to be on a safe side should mold contamination result from this damage in the future.
Both estimates are fair despite a big price difference. This is where you have to specify what your biggest concerns are.
Contractor may misestimate square footage, amount of materials needed, forget to include certain steps of the process in his proposal etc. At the end we are all humans.
How do you pick the right estimate?
Follow industry standards.
There is a preset price range in place for almost all construction services.
“Bluebook residential cost guide” (available at libraries) contains accurate pricing data. Use the scope of work and square footage usually outlined in the written estimate from your contractor(s), calculate everything then reference the blue book and get your fair estimate result.
To simplify the process you can also use an online cost calculator like the one at www.homewyse.com . Just plug in your numbers click calculate and voila! Instant carnage.
Construction estimating has nothing to do with quantum physics, Fermat's last theorem. It is a simple process that involves basic math and some data from the open sources.