Ok, pretty much everyone knows my position on the Welker-Amendola situation, so you know this isn't coming from the pro-Bill side of this particular equation:
The one edge Amendola had over Welker is that he's a bit more flexible with regards to outside play. Welker can do it, but he's clearly much less comfortable on the outside, while it's not an issue for Amendola. The significance of that is that there's a greater interchangeability with Amendola/Edelman than there was with Welker/Edelman.
Amendola's not going anywhere in 2014, because his contract prevents that from happening unless the Patriots are willing to take a $6.8m cap hit in order to avoid paying Amendola $4.7m. Since the cap is not expected to rise much, yet again (Brilliant CBA work, NFLPA.... Dumbasses), that would be a significant impact on the Patriots cap space.
That being the case, keeping Edelman around allows both for a theoretical 2 player punch and built in redundancy for when one of them ends up on the shelf again. As long as Edelman's not asking for an unreasonable deal, it makes sense for the Patriots to bring him back and have both on the team.
Amendola's cap situation becomes palatable as far as cutting for cap space beginning with the 2015 season. If his body has him on the shelf again next year the Patriots can cut him loose before that 2015 season and at least gain $2m in cap space.