It's for the convenience of being able to write/play with headphones and record with the same unit. I use headphones a lot so I really like the added jacks myself.

But Timbob is right. They're the same part I believe. I use a much thinner gauge of wire and it's solid core so you it's very easy to run in through the case of the Game Boy and keep it where you want it. And it is sealed with glue so your wires don't break off the jack. You only need to solder 3 points which are fully described on the product page.
I also have a bunch of other cool, affordable kits you could pick up to try out!

Two jacks are actually really helpful! If you connect your prosound post-pot, then the stock headphone jack still has built-in volume control. It can also function as a sort of headphone monitor jack.

Why does almost everyone add another jack? I prosound the stock one and it sounds fine

Flip a coin...

they are exactly the same, but one has a wire already connected, and the other doesn't
if you are fond of doing the wiring yourself, pick the non one.

otherwise, get thursday's kit.

It's not like one will give you better wubs than the other.

Im stuck right now, Between buying nonfinites pro-sound kit and Thursdays customs, i have never bought one of these and i dont know if one is better than the other, so im hoping you guys will help me :3

http://www.nonelectronics.com/catalog/i … 61fc775020

http://www.thursdaycustoms.com/product/ … -sound-kit