Depends. What are their tastes? What kind of time do they have for videogaming? How good are they?
My highly unscientific recommendations:
Hardcore gamer, loves big challenges, attracted to games with lots of hype, wants lots and lots of playing time in every game, wants top-of-the-line graphics and sound, really into online gaming, isn’t turned off by a history of notorious unreliability: XBox
Hardware-wise, there’s simply nothing that can compare to the computer company-created XBox, and the vast majority of the games have a whole lot to them and take a long time to get through. A lot of megatitles, like Halo, are also on this system, most of them exclusives. There isn’t a whole lot for the casual or even oldschool gamer (like me), so only get this for someone who has no bones as to what it’s about and will appreciate it.
Young/casual/inexperienced gamer, prefers “lighter”/less serious titles, attracted to cartoony graphics and bright colors, doesn’t need/care for mature-themed games, doesn’t mind unusual controls, prefers relatively short sessons (say, 10-20 minutes), wants something reliable and with few performance issues: Gamecube
Despite Nintendo’s halfhearted efforts to shake the “kiddie” label, the Gamecube’s game list is the most family- and child-friendly one of its generation by miles. Lots of party games too, and the ideal system if you’re getting one for the entire family. I’ve never heard the reliability horror stories that have plagued other systems or a laundry list of problems loading or running games, so if dependability is a big issue, this is your system.
Likes a tremendous variety of games, wants a balance between capability and cost, wants lots of peripheral support (and is willing to spend a lot of money on this), wants easy availabilty of system, games, and peripherals, isn’t too concerned about online, is willing to put up with a little slowdown and slow loading for some later titles: Playstation 2
As a longtime PS2 owner, I can attest that this is a system that can do it all. The trouble is that in recent times some companies have tried to do a little too much, to the point where some of the old problems near the end of the PS1’s run (especially slowdown) have cropped up. Also, if you want to play imports, you really have no good choice other than to shell out for an import system, as all the modding or disk swapping options come with all kinds of problems. Reliability wise, it’s well behind a Gamecube but still miles ahead of an XBOX.
As I haven’t the slighest idea what 13-year-old boys want, I leave the decision to you.