Will might be more happy and relaxed in the second photo because the environment of the recent photo was more jovial and less severe.
However, it doesn't seem fair to place all the blame on Will’s mom for their gloomy photoshoot. As Will tells his brother, the photoshoot has come about because their mom wants to have a picture in case something bad happens to them. Remember, the shoot occurs only a week after the death of their dad. Even though Will can't remember his dad, it's still his dad, so his death carries a serious significance. The grave context makes for a somber picture.
Adding to the unfortunate atmosphere of the shoot is the clothes that Will and James have to wear. Even though it's hot, Will and James are forced to put on uncomfortable wool pants and shirts.
The photo session with Joyce Blue Horn's family unfolds in an opposite fashion. There is no mention of uncomfortable clothes or family deaths. While it comes across as rather wild—with Will setting up the timer and then running to be in the photo—the mild disorder seems to lead to a good time, as evinced in Will's smile. Indeed, the childhood photo has a funereal air and the recent photo has a festive feeling. The different climates are probably what account for Will's divergent dispositions.