If the water is bad, then why isn't the other Betta suffering?
Could this be from being closed up in a plastic container for a long time at Petsmart?
All fish are individuals, just like people and animals. Some are genetically stronger than others and tolerate conditions better than others.
The new fish could have spent more time in poor water at the shop or breeder and is weaker due to that.
It might not have received as much food as other fish.
The fish could also be suffering from stress due to water chemistry changes over the last week or so. The fish might have only just arrived at the shop shortly before you bought it and it might have been in different water at the shop and is in different water in your tank. All these factors add up and contribute to a weaker fish.
The following link has information about what happens to aquarium fish when they are shipped from fish farms to the pet shop. The fish go through a lot of stress and are exposed to lots of different water conditions during that time.
http://www.fishforums.net/threads/fish-importing-from-the-farm-to-the-home.451553/#post-3813924
The best thing for all fish is clean water, clean tank, and clean filter.
Do water changes, gravel cleans, make sure the filters are clean, offer a variety of food and feed him 3-5 times a day to try and build him up physically. Fish that are well fed have more reserves to fight off diseases. A month after he has recovered, you can reduce his feeding to once or twice a day and reduce water changes.