I would like to start by pointing out that Doom did not have a nice arsenal of pass rushing moves. I always saw him trying to gain the edge relying on an explosive first step and bull rushing if he didn't gain that initial advantage, hence the false start penalties..He's not going to be irreplaceable..
I also don't want to over pay for anyone that's currently available..
Now let's start with Freeney. He has multiple effective pass rush moves, the spin, the swim, the edge, and what player can't bull rush. But Freeney is a shell of his former self and is an even bigger liability against the run than Doom. He's also selfish and all about his stats, which is good in that he's QB hungry, but bad in that he will leave car length gaps exposed to the run game. I would be fine with Freeney as a situational pass rusher but not as a starter. I don't like the predictability of Freeney and how he can be exposed in a hurry up offense.
Abraham is an effective player against both the run and rushing the passer and wouldn't be exposed against the hurry up offense. He has somewhere in between Freeney and Doom with pass rush moves. Abraham seems like a quality fit, but he really has father time working against him.
Personally I think it's best to draft a DE, and let Ayers/Jackson compete for the base downs. The front office should most certainly be looking for a more complete DE, which is why I am hesitant to replace Doom with Freeney. Abraham hasn't shown signs of wearing down.. And getting a ring can revitalize a player see Michael Strahan. My preference would be Abraham because his only limitation is time. But we should be developing a long term answer there anyway.
Other options are Phillips, Harrison, Idonije* or a trade for someone who doesn't fit a scheme, DB4L mentioned Trent Cole and I thought that several weeks ago before looking at the contract. So unless a player is released I'm very iffy on a trade.
Idonije is a cross between Abraham, Doom, and Ayers. Abraham because he's solid against both the run and pass, Doom for the BULL Rush, and Ayers for probably being projected better as a strong side DE. What I like about Idonije, is that he had 3.5 fewer sacks than Doom in 300 fewer snaps. Idonije is that complete DE I think we are searching for. He has faired pretty well facing one on one match-ups with Peppers being their Von. The issue I have with Idonije is that he's a slightly further along the curve and more complete version of Ayers, who can potentially be the same player, so I wouldn't waste the money..
In conclusion I would prefer Abraham on a short 1 or 2 year deal if using what's left in FA to address the position. But I would be content with letting Jackson/Ayers compete for the base down work, and a drafted DE/or even Beal used in sub packages as Freeney would be. Let's save the money, develop our own or use the draft. Or bring in Abraham and still develop our talent/use the draft.