Full disclosure, I have both systems – Wii and PS3. And I am far older than 15.
If your child is someone who’ll become comfortable or OK with monitoring (both content and time), I’d recommend the PS3. It is a much better deal than the Wii, since it can play DVDs/CDs and games in HD and has a hard drive where you can store pretty much anything (like photos). YES, it can be connected to the internet, BUT so can the Wii, PLUS the PS3’s connectivity is NOT designed for a great web browsing experience, rather so that one can log into Playstation Network (PSN) and buy content from there. There are some very good, entertaining, wholesome games on PSN. Just because something can “connect to the Internet” doesn’t mean you could or would want to do the same thing on that connected device as you’d on a PC.
The Wii is a fun console, content offering for it are a little thin and it doesn’t have the visual and aural “pop” that PS3 content does. I’d recommend a Wii if a family was looking into a family console, but a teenager wanting to buy one is different, if monitored OK, I wouldn’t want to see him sink all that $$$ into a console he’ll use for a month then discard.