Bold prediction. PS4 will beat 3DS week 1 of its existence.
Seriously 3DS will probably outsell it. It's a Nintendo handheld and it owns the market. PS4 will have stronger competition and more of it. Also PS4 will cost a lot more (over double) so I would hope it doesn't sell as much. PS2 still managed to beat out less expensive handhelds so I guess there's a chance but unfortunately MS is still around so it won't be as universal in the home console market as with PS2.