After a record-setting six seasons with the Patriots and Tom Brady, Wes Welker will be catching passes and bouncing off tacklers for another team and quarterback — New England nemesis Peyton Manning. Welker on Wednesday agreed to a two-year contract worth $12 million guaranteed with the Denver Broncos, one of the Patriots’ chief rivals in the AFC. The Patriots moved quickly to counter the move, signing former Rams receiver Danny Amendola to a five-year contract worth $31 million, of which $10 million is guaranteed, according to a league source. Amendola, 27, is 4½ years younger than Welker, 2 inches taller, and more athletic after the catch, similar to Julian Edelman (also a free agent). But Amendola, who had a career-best 85 catches in 2010, has missed 20 games the past two seasons because of injury. Welker missed a total of three in his past eight seasons. Why did it come to a divorce between Welker, who was beloved by fans and teammates, and the Patriots?