Punt returning requires such super quick decisions, instincts, and field sense.... experience and physical quickness also have to be key. Edelman is the perfect fit, I think, but I hate the risk which adds to all his other risky receiver routes.
The only questions I have about Amendola: 1) Isn't he more injury prone? 2) And more likely to fumble?
I love Edelman, and he's an incredible weapon as a punt returner. But I think we need to be situational about it. The difference between him (top 10 returner) and Amendola (around 21st among regular returners with at least 10 returns last season) is only 4 yards per return. If we're up 14, might as well let Amendola out there. If it's a tie game late in the 4th, maybe put Jules out there.
As for the fumble risk, I was wondering that myself so I took a look. Some of these sample sizes are really small so I wouldn't draw anything conclusive from them, but for what it's worth...
Receiving
Amendola: 279 catches, 4 fumbles, 1.4% fumble per play
Edelman: 277 catches, 2 fumbles, 0.7% fumble per play
Rushing
Amendola: 13 runs, 0 fumbles, 0.0% fumble per play
Edelman: 25 runs, 2 fumbles, 8.0% fumble per play
Kick returns
Amendola: 138 returns, 1 fumble, 0.7% fumble per play
Edelman: 26 returns, 0 fumbles, 0.0% fumble per play
Punt returns
Amendola: 107 catches, 5 fumbles, 4.7% fumble per play
Edelman: 132 returns, 10 fumbles, 7.5% fumble per play
Totals
Amendola: 537 touches, 10 fumbles, 1.9% fumble per play
Edelman: 460 touches, 14 fumbles, 3.0% fumble per play
It's obvious that punt returns are the most significant fumble risk for all plays. Kick returns seemed incredibly safe, and Amendola's numbers are inflated by having 5 times more of the safer play. But even if we remove kick returns from the equation, Amendola's fumble rate is around 2.2% while Jules is around 3%. It's not a huge difference, but at the very least, I think we don't have to worry about it being more of a fumble risk, but again, small sample sizes.