My basement flooded and a water mitagation cut out 1foot of drywall throughout the basement walls, the basement is approx 1100 sq feet. I had 2 contractor give me estimates, 1 contractor stated that he would replace just 1foot of drywall throuhgout the basement The other contractor stated that to do the job properly, he would cut out the drywall 4ft high and use whole sheets, so that the seems will line up properly. My question is which contractor is right and what is the best way ?

Both are right. The best way is what the contractor thinks is best way for him. The result for you should be the same.

Contractor 1 believes it is the least work and material to cut the
the existing at a reasonably straight line 1' above the floor, cut the sheets of new drywall into 1 X 8' strips. This has the advantage of using less material and the handling of smaller strips. It also has the advantage of most likely avoiding cutting out for any electrical outlets. It's disadvantage is the time and work of cutting the old drywall reasonably straight and parallel to the floor. He must also insure that his cut is above any damage material. Another disadvantage is that the finish work must be done down on your knees.

Contractor 2 is saying that the material is cheap. Its faster and less work to simply rip the lower panel off the wall, breaking it at the joint line. Clean up any joint compound he can on the upper panel and nail up a full sheet. He will of course have to cut out for outlets and will have vertical joints to finish. Most of the finish work will be at waist level. He will have more damaged drywall material to dispose of.

Properly finished the result to you is the same.

The only thing that I can see that might make a difference would be insulation. If insulation is involved and has gotten wet it should be replaced. How is contractor 1 going to handle that.

What is the price differential? With a 1 ft. section added to the bottom, the seam will be feathered out and not noticeable.

There is no need to remove 4' if damage is only 12" or less. You will use 4X the material to start with. It is much easier to cut lower, removing at seam means having to remove all the existing drywall tape which can be time consuming. The new 4' tape joint is closer to eye level, if there is any type of a texture finish on the wall it will have to be matched. It will need to be "feathered in" most likely to 5' - 6' high. Replacing the bottom 12" puts the "patch" or "feathered texture" at a much lower level. It can be difficult at times to match things perfectly, by having it lower than eye level it helps hide the patching. Your contractor will have to verify that the water damage does not exceed 12". They will also have to replace damaged insulation. if it has been wet withing the last couple weeks I always recomend leaving the area "open" a few days with a fan to help dry the area completly before closing it up. The cost in materials could be a big issue. If you had 100 lineal feet of basement walls for example. To replace 4' it would take about 13 sheets of drywall. To replace 12" it would take 3 sheets. The taping compound would also take more. It could mean a difference of $150.00 or more in materials alone. The disposal cost will also be greater. In my opinion if you can verify the damage is 12" or less you would be better off removing 12" verses 48". Repairs would be cheaper and quicker, would also be much less visible if the matching is less than perfect.