We don't know specifically how Amendola will be used in the offense, although the sense here is that his role will mirror Welker's in some elements. In St. Louis, Amendola was both a "Z" receiver (aligned as the outside receiver to the tight end side of the formation, one yard back from the line of scrimmage) and slot receiver, much like Welker was in New England.
What we do know about Amendola is what we've seen off of his tape study from previous seasons, highlighted below.
Positives. Amendola has terrific short area burst and quickness and is an exceptional route runner. He is light on his feet at the top of his routes and in his breaks, and is an elusive player who can slide through crevices between defenders. He is comparable to Welker in many of those ways. He has better long range speed than Welker, though he lacks the leaping ability and length to leverage defenders down the field. He has very good hands and vision, and is an effective run-after-catch player. He has exceptional balance and can torque his body near the sideline to make tough catches.
Limitations. The biggest concern with Amendola is his ability to stay on the field. He's missed 20 games in the past two seasons due to two major injuries, both to his upper body. He doesn't lack toughness, however, as he played through extensive pain in 2012. He's not an elite vertical threat. In New England, he'll need to establish a rapport with Brady, something the quarterback had with Welker.
Assessment. It's easy to see the allure of signing Amendola. His skill set aligns with what Welker brought to the table, with the biggest difference being Welker's ability to stay healthy. The Patriots are banking on Amendola bringing a similar consistency. If he can stay healthy (something that is unpredictable), Amendola has the necessary traits to be extremely productive in the Patriots system (a 100-catch receiver). The Patriots are going out on a limb by letting Welker walk to a conference rival, but the upside of Amendola is extremely high.