This is a no-brainer..
I like Noah, but his ceiling is a high-end role player..if you can get a top 10 player in the NBA that is either in his prime or about to enter his prime, you obviously have to pull the trigger..
The Bulls aren't going to win a le this season no matter what they do..so they're thinking about the present AND future..if Anthony is going to sign an extension, of course you do it..
What would be better?..
Year 1: Keep Noah, which fills the hole at C and might make the Bulls a better team for this season..however, this team doesn't have as high of a ceiling, as they still only have 1 potential star player, and he plays the PG position, which hasn't been successful for championships as of late..
Year 1: Keep Anthony, have a hole at C, and maybe have a worse team than you would with Noah..however, for the future, you can have Carmelo Anthony, a top 10 player in his prime, AND THEN you can fill the C hole the next year, which obviously gives you a better team for the future..
I would definitely be willing to sacrifice a year and be a little worse for the sake of having Anthony for many years to come, since the Bulls could just fill the C hole the next off-season..granted they probably won't get a better player than Noah, but you just don't pass up a star wingman in this era..