Earlier this week, I helped my friend change the pair of pickups on his new guitar. When we completed the change, the neck pickup was MUCH louder than the bridge pickup. However, he told me it wasn't new and that the guitar already did that with the stock set of pickups.
Since the pickups already did that, I'm guessing they aren't faulty. Would anyone know what could be the problem here? I am guessing it's the switch, but I'd like to actually be sure so I can help him.
That's normal. Neck pup's louder than the bridge pup.

To compensate, you do one of the following:
1) Use a bridge pup that is hotter - I guess that's out of the question here.
2) Adjust the bridge pup to be closer to the strings. Typically, you set the bridge pup to a height that you like, then adjust the neck pup until you get roughly equal output.
How much out put is the neck p/u?

Is the neck p/u really close to the strings? This is often the case.

How close to the strings is the Bridge p/u?

Is the p/u wired correctly? This happened to me on the 1st p/u change I did and it was because I didn't wire the p/u correctly. It was easily fixed though.
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We don't know for sure about the output. However, the pickups are both from a strat set, and are supposed to work together. As for the volume, it's a huge lot of difference, not anything normal. I own a lot of guitars, and this kind of difference only happens on my Gibson SG (and I've always felt it could have a problem as well).
Also, it is a pretty cheap guitar, so the parts aren't exactly amazing...
Well, try resoldering all the connections. If that doesn't help, hard-wire one pickup to the output, see how it sounds. Desolder, then wire the other one straight to the output. See if there's still that big of a difference.
If yes, the pup's borked.
If no, start adding the other parts to the circuit until the problem comes up again.
Are the pups connected to seperate volume-pots? Chances are the pot the quiet pup is connected to is just screwed up.