My first question has to be, "What the heck are you tearing up and putting back together again? A dollar bill? a Playing Card? Napkin? Newspaper?"
My second point has to be that there is no "best" outside the one that works best for you that supports your persona and the artistic expression of the act your are presenting. If I do a Newspaper Tear it will usually be the Anderson Tear but I've used a couple of others over the years because of how they lend themselves to the routine and the feel of the act that I want to bring out.
On the close-up level I've only done a rolling-paper tear, Harry Anderson's Mismade Dollar routine and the comedy Napkin tear on any regular basis . . . never tried any of the clever playing card routines that have come out in recent times though a couple of them are quite amazing, so I can't speak to that niche.
Pardon the rant but we old guys get our shorts in a twist when there's little to no clarification. . . I only play a mind reader on TV, I have problems when it comes to the internet and understanding WTF magicians brings up. . .