The different door hinges are because of the different face frames. On the first picture, look how close your front frame is to the interior cabinet wall. Maybe 1/16th of an inch. He's able to use a frameless european hinge. Quick term: frame refers to the front trim pieces that attach to the actual box of the cabinet.
Now look at your second hinge photo. The face frame comes out about 1.5 inches from the wall cabinet. He went with a frame design that rests of the front of the frame, causing your gap. So he's 'right' that he can't adjust the second hinge to make a nicer gap. He's wrong that there is nothing you can do about it. He got lazy/cheap and didn't want to buy hinges that are for frames that don't sit on the outside of the frame. He could have put blocking behind the frame, making it flush with the frame and allowing him to use a frameless hinge if he wanted to as well.

Google full frame european hinge as well as frameless european hinge and you'll get the picture. Those hinges aren't cheap, so he could have done this to use whats in his bag, versus buying very specific hinges for your purpose. Because the hinge designs that can go around frames are designed for very specific frame widths. The ones he used are nearly universal.
Technically, he used a frameless european hinge on the first cabinet where you're not supposed to, on the frame. He can get away with it because of how tiny the frame gap is. Still wouldn't be thrilled, there are other designs that use 4 screws and mount to the interior wall that will last longer to the rocking back and forth motion. In the second photo, he could have used to the same hinges, BUT it would have pushed the door leftward and flush with the frame as opposed to concealing some of the frame behind the door like he's done with the the hinges that sit on the frame.