I just noticed I forgot to mention... Why does the Enclave in Fallout 3 have the radio station and place signs and posters to recruit/convince people that they are good guys... I mean... Why? They want to kill everyone in the wastes, so why are they wasting resources sending several eyebots with their radio into the wastes or making signs like this:
There is a reason to advertise yourself and promise a lot of good things to people. It is to make them like and support you... But what is the point when you will use a virus to wipe them all out quickly while they don't even know if you really exist or not?
Compare that with the Enclave of Fallout 2. They are secret, they do things in secrecy. They don't announce their existence to the world until they are in their final stages of their plan (and still they don't announce themselves, it was lucky they left Hakunin behind because they thought he had died or no one would have ever known about the Enclave until it was too late).
Secretive Enclave makes a lot of sense since they were the Shadow Government before the bombs fell. During their history, their entire success have been because no one knew they existed. They failed in Fallout 2 because someone found out they were there and stopped them... So why would Eden go against the Enclave philosophy of moving the pieces behind the scenes that was what always allowed the Enclave to succeed and survive? Specially since there is absolutely no advantage in letting the Wasteland know they exist.
Even in terms of gameplay, if Fallout 3 didn't show or told you that there is a Enclave in the game as soon as you step out of the vault (there is an eyebot playing the Enclave radio just a few steps from Vault 101), and all of a sudden they appear out of nowhere on project purity, it would be a much bigger impact/shock/surprise the first time we play the game. Instead we just go "Oh, those must be the Enclave everyone and their dog talk about and advertise themselves everywhere.", while we could be going "WTF! Who are those guys in highly advanced looking power armor!?" (for those who never played the Fallout 2) or "WTF! What is the Enclave doing here!?" (for those who recognized them).
Also imagine if the Enclave was hidden in Fallout 3 and no one knew they were there, then during the end of the game we found out that the Enclave had a spy in the Project Purity team. James only knew about the GECK because the Enclave somehow hinted it's existed, that the Enclave killed James wife by injecting her with the altered FEV hoping to kill her and the baby (maybe because James had mentioned that he wanted to move to the vault so his kid could have a safe future) so James wouldn't abandon Project Purity. Maybe even make James' wife being the Enclave Spy, but she actually fell in love with James and after the baby was born, she planned on telling James about the Enclave, so they poisoned her with the FEV without her knowing.
We then find out that they have been manipulating James to make Project Purity a reality from behind the scenes, just so they could then use the FEV on it. Now that sounds like the Enclave methods...
You could even throw in the Super Mutants being because the Enclave made a few using the facilities of vault 87 and gave them the means of making more, just so it would keep the BoS busy, so they wouldn't meddle with the Enclave, or find out the Enclave was there or whatever.