How do I replace a storm door when I have a cracked door jamb?
I agree with Jeff Widmer -- you don't need a bigger/stronger bracket, as it's not the bracket that failed, but longer screws to properly fasten the bracket.

Given that, your jamb repair doesn't need to be structural so don't sweat how strong it is and just make it look nice with whatever product you've used before and liked.  After you drill your pilot holes for the new bracket screws, drill out the repaired jamb with a bit that's larger than the screw threads so the screws don't stress your repair.  Of course you want this larger hole to only be the depth of the jamb, maybe 3/4".