One is not better than the other. They serve different purposes. With a vet school or specialty hospital each vet is highly specialized in one area. They also have more diagnostic equipment to use.    
For instance, does your general vet have an endoscopy unit to take a look in there? And just as importantly are they proficient in it?   
Cody should absolutely see an internist at this point. Vet schools do have the disadvantage of students hanging around, but remember the ones ultimately overseeing your pup's care are their teachers. Your pup won't be in danger in this setting. If you are still uncomfortable you can go to a large referral hospital. Nearly the same minus the students...   
What has your vet tried for this?     
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