No, I don't think the Patriots are better without Faulk, HOWEVER...
I do think the Patriots have a lot of potential to improve their offense, more than other teams. They have some young players whose confidence could catch up to their physical skills in Gronkowski, Hernandez, and Tate. I think that, even with the loss of Faulk, the offense might be better at the end of the season than it was at the beginning.
I want to point out, also, that the Torry Holt injury hurts more than most people will allow. I do not think he would have been cut, and he would have been an excellent veteran presence for Brady as a third option, splitting time with Tate. I think Brady still feels that there are only two trusted players out there in Moss and Welker, and losing Faulk hurts there. Hopefully Gronk and Hernandez will continue to play out of their minds, as rookies go.