The issue is not 3-4. Its more one-gap versus 2-gap. The Steelers play a one-gap and Belichick and disciples play a 2-gap (even when they go 4-3). The one-gap still allows for the penetrating Le beau type player, especially in the LB corps. Belichick's disciplined system is strictly read-control-react.
To play Belichick's system you need big, tough, Defensive linemen, who are good enough that they can play read-react, take a blow, and still play as if they were one gapping. That asks a lot, and consequently we have 4 #1s and 2 #2 and a #4 as our DL for three positions.
As far as the LBs are concerned, Belichick's system is read-react but don't free lance. He can than get away with slower players (ie. bigger, older, experienced, sage, vets preferred) but only if no free lancing is enforced otherwise holes open up and the other players are too slow to be able to close them against a good running game.
Vilma will have problems, I predict. But his talent should allow him to beef up over the next season or two and he'll be fine.
As a backup to Vilma, I am not surprised that Gardner seldom saw the field. How come he got a start? Was Vilma dinged up? And how did he do that game? My theory is that Gardner was just the type of vet that Belichick turns in to a minor star. The profile: A former high pick who does not excel but is smart and willing to work hard as exemplified by ST experience. These guys can play disciplined ball, and carry out their assignment which is drawn up to be not overwhelming athletically, and that is all that BB really needs. Examples are Phifer and Vrabel who were not anywhere as "good" as they became with the Patriots in their late twenties and thirties.