The difference is Obama's plan specifies all funds are for SECULAR use only. No funds for religious activity. The Bush plan said that in the Announcement but by the time it became law, it was overburdened with religious spending issues, caveats on who could get money, what they had to do, what message they HAD to project. It was Conservative Social Engineering.
With the Bush Initiative, if it had existed as promised during the campaign, and at the announcement of its creation, there would have been a much different respect for that president. But, like much of the rest of his promises and agenda, once he and his Republican Congress tuned up the bills, a blanket NeoCon agenda emerged.
Take the announcement you posted and then survey the actual programs and see just how many of them were "as advertised". THAT was the problem.
He was instantly vilified, though, at the suggestion of his faith based initiative. There are many links to Google through, this one was one of the first (from 2002) and it suggests no such religious agenda:
Faith-Based Initiative: Current Status - Page 2
FWIW, I am not a fan of the faith based label or singling out such groups, too much opportunity for a constitutional violation. Had he advocated private charitable organizations to take over the work of charity that the fed does, it would have been far more palatable for me and likely others. Wouldn't have to exclude any particular organization, in fact, just give the tax $$ back to the citizens and let them choose, eliminating the possibility of church and state issues and accomplishing charity the way it was intended.
But, the point remains, when GW suggested it, even if it was later ruined, the left jumped on him immediately, and his suggestion was very similar to what BO is suggesting now. He deserves the same treatment, not a free pass to see how it shapes up.