CK wrote an excellent piece on it. Instead of linking it and having to scroll to the post, as it's a little messy in that thread, I will copy the post for you here. Easier for me rather than getting all into it which would be time consuming.
CK POST
Gibril Wilson already said on a radio interview that the Dolphins will be using a Quarters base coverage.
The Quarters defense is a Cover 4. It was a specialty of Jimmy Johnson's, a coverage that he used with the Hurricanes, Cowboys and Dolphins. When Dave Wannstedt took over, Miami went to a Cover 2 instead of a Cover 4.
Cover 1, Cover 2, Cover 3 and Cover 4 refer to how many people you have responsible for the DEEP portions of the football field.
A Cover 1 means you have man coverage on the outsides and you have one safety responsible for protecting the deep middle third of the football field.
A Cover 3 means you have both corners responsible for the deep third of their side of the field, plus a safety responsible for the deep middle third of the field.
Cover 3 and Cover 1 are often interchangeable, because the only difference between them is the corners will come up and play man coverage on their receivers, or they will keep everything in front of them and play zone.
A Cover 2 or "umbrella" defense is when you have the deep portions of the field split into two zones, and one safety covers the right half of the deep field and another safety covers the left half. The corners can play zone or man in a Cover 2. When Jimmy left, Miami played a Cover 2 where the corners played press man underneath the umbrella. The Tampa 2, on the other hand (and most classic Cover 2 defenses) have the corners playing zone, keeping the receivers in front of them and always keeping their eyes on the Quarterback.
A Cover 4 is where you split the deep field into four zones and have both safeties and both corners responsible for a Quarter of the deep field.
So, what are the benefits of a Cover 4?
Well, for one thing BOTH safeties can be more active against the run. A Cover 3/Cover 1 is designed to where you have one safety that has a deep third responsibility and another that has some sort of underneath responsibility whether that be a robber zone or man coverage...but either way the guy that is supporting the run is always just going to be one safety and it's the other safety's job to always err on the side of caution defending his deep third.
In a Cover 2, safeties are responsible for a whole half of the deep football field, which is a wide area of responsibility, and so it can be difficult for those safeties to come up in run support. Fortunately for a team like Indianapolis, Bob Sanders has legitimate 4.3 speed and functions like a human missile. He reads his run/pass keys very well and has the speed and physicality to get right up and be aggressive in stopping the run.
In a Cover 4, the deep coverage responsibilities of the safeties are not very onerous. They each just have a Quarter of the field to keep an eye on, rather than a third, a half, or a whole field. This affords them the ability to use their first couple of (slow) steps to read the run/pass keys to their side of the field, and then both be very aggressive in coming up to stop the run. This is why Miami has two safeties that many think of as "strong" safeties. Both guys are smart and aggressive players that will come up and hit the ball carrier, stopping the run.
Another strength of the Cover 4 is that it can be disguised more easily, and mixed with other coverages, in order to cause confusion on offense. You can have your cornerbacks come right up to the receivers like they will be in press coverage, and with both safeties back at even depth, a Quarterback is going to read Cover 2. Against a Cover 2, with the safeties each having responsibility for a half of the deep field, they will generally be slower to get to the sidelines to help out a corner. Throwing the fade is one of the ways to throw into the "hole" between the zones, against a Cover 2. The problem is, if it's a Quarters or Cover 4 defense, that fade pass is likely to get picked off. On the other hand, let's say the Quarterback is onto your Cover 4 even though you're giving him a Cover 2 look with your corners up. One predictable way to hurt a Cover 4 is to throw out to a back out in the flats. So let's say the Quarterback decides he is going to do that, thinking you're in a Cover 4. But, what if you decided to truly go Cover 2 zone this time? Again, pass gets picked off.
Moral of the story is, the pass drops for the DBs in a Cover 4 are very simple and not terribly difficult to accomplish especially if you have size and speed on your side, and so you can play around a lot with the pre-snap formations and alignments in order to foster confusion on the offense, and then you can mix it up with other coverages to keep them on their toes. This lends itself to a 3-4 defense because a 3-4 defense is designed to mix up its pass rush looks in order to accomplish the aim of getting pressure on the QB. It's one more thing the QB has to think about and the more you can give him to think about, the more chance he'll make a mistake.
The weakness of a Cover 4 is the underneath areas. Cover 4 DBs keep the action in front of them at all costs. This leaves some underneath areas open particularly on the edges of the field. You can't have guys missing tackles. That's a big no-no. Also, your safeties are going to be aggressive in their run/pass keys so they will be susceptible to play-action fakes. This means your Quarters cornerback has to have the athleticism (and size) to run with a receiver on a play-action post pattern and defend that deep ball.
The key is squeezing this opportunity area as much as possible, not allowing big pass plays, not missing tackles, and stopping the run. Stop the run and you're going to put the other team in predictable down and distances, and you can get funky with the things you do to them. If you're stuffing the run and you're not allowing big pass plays, the odds are not favoring the other side scoring points on you without making costly mistakes.
The coverage responsibilities of both safeties are smaller than in a Cover 2. And in a Cover 3, one safety is always going to be erring on the side of caution with respect to his deep portion of the field.
In a Cover 4, both safeties can be much more aggressive in their run/pass keys. And, if they have 4.4 speed (as both of Miami's safeties do) then once they read their keys, they can run the alley very quickly in run support.
There's a high school football coach on another message board that explains it better than I can. His favorite defense is the Quarters defense. He has learned from some people that are connected with Jimmy Johnson and share his affinity for the defense.
I have to hand it to him, when Miami signed Gibril Wilson to play safety opposite Yeremiah Bell, he absolutely nailed the prediction that Miami would be going to a Quarters coverage. It didn't take long before Gibril actually confirmed as much on a radio interview.
I don't think anyone is giving anything away, when you have two safeties that look a lot alike, this lends itself to a Cover 2 or Cover 4...rather than Cover 1 or Cover 3. And, when both of those safeties are guys that are good run stoppers, well...that's Cover 4. I believe the Giants played a lot of Cover 4 in 2007 when they won the Super Bowl...and Gibril Wilson played well in that coverage from a spot that many confused for a Free Safety. I think Cover 4 lends itself more to the Left Safety/Right Safety split than a Strong Safety/Free Safety. In Oakland, Wilson was a Strong Safety and a real wrecking ball against the run.
Traditionally you didn't use a Cover 4 in connection with a 3-4. As you say, it's more popular with a 4-3. I don't know for sure, but I think this is because a 3-4 is inherently strong against the run and weak in pass rush, while a 4-3 is more inherently strong in pass rush and weaker than a 3-4 against the run.
One of the strengths of the Cover 4 is supposed to be the fact that both safeties can aggressively stop the run. On the other hand, there are pass completions to be had underneath. This would mix well with a 4-3 because with 4 quality, one-gap defensive linemen rushing the heck out of the passer, if the QB keeps taking the underneath stuff against a Cover 4, eventually the pass rush is going to get to him and create a costly negative play. So, that's supposed to be a good marriage.
On the other hand if one of the strengths of a Quarters coverage is stopping the run, and you marry it with a 3-4 defense that is, by design, inherently a run stopping defense...you're marrying strength with strength and I suppose some would wonder why you're doing that. Also, you're mixing a secondary coverage that allows a lot of underneath completions with a pass rush that is less dangerous than a one-gap 4-3. So you're marrying strength on strength and weakness on weakness, rather than strength-weakness, weakness-strength.
That's my GUESS as to why it has traditonally been married with a 4-3 defense.
However, so says the coach who explained it on another message board, recently it has become a little more popular to marry the Quarters coverage with a 3-4 defense. This could be an indication that players are getting to a point where pass rush is no longer an inherent disadvantage of a 3-4 defense. But also, it could be because the 3-4 fronts are so multiple and unorthodox in their pass rushing, and a Quarters coverage is by design supposed to be good at fooling Quarterbacks...that maybe marrying those two strengths together will overload Quarterbacks mentally and cause them to make mistakes. This could cover for the fact that you're mixing inherently weak pass rush with inherently weak underneath coverage...and give you the promise of severely stopping the run, and then also stopping the pass. You just have to win the chess match.
