Bang on Noodles.
Billups is a great PG, no doubt. In fact, he would be a perfect acquisition for the Lakers as he'd fit the triangle perfectly. He's great at running offenses and being a 3pt threat. He's never been an athletic guy nor that fast, pick and roll just isn't his thing. Amare needs the pick and roll to get his 15-20 points a game. You can't give him the ball at the low post and let him do his work, he just can't.
Melo is a great scorer no doubt, but does most of his scoring via isolations either from the perimeter or in the high post. He doesn't defend as well. The problem now is with the Knicks offense, which essentially is pick and roll / drive - kick, you will have to alter that and allow for Melo to do his work. Melo isn't a great spot up shooter like Ray Allen. He needs the ball in his hands to score. Since he never really plays pick and rolls... what's Amare gonna do? Felton looked amazing in the Knicks offense cause the way he plays suits the Knicks. Much like Nash would be awesome for the Knicks. Now he's traded someone where Pick and Roll isn't played much, he won't be useful anymore...
They won't get Paul because they don't have the cap space nor the assets to trade for him or acquire him as a free agent. He'd have to accept around $10m to play for the Knicks, not even he's that desperate, especially if you could be earning $17m-$20m elsewhere, the money is just too much to pass up.
All up, the only people that think this trade is a good thing for the Knicks are delusional Knicks fans who are blinded by the bright lights and uninformed people who think basketball is all about points and stats.
The Knicks lost some players with real good upsides in Chandler, Gallinari, Randolph and Mozgov. The best thing they did was drop Curry's contract. That's about it. Oh, and they'll get a boost in hype and marketing... But no D, no championship.