Since the arrival of Mike Nolan in Miami, the Dolphins have implemented a base 3-4 defense while still running a 4-3 formation at times. With the arrival of Kevin Coyle as Miami's new defensive coordinator, it is expected that he will bring the 4-3 defense that the Cincinnati Bengals ran during his time there. 
Miami has been building it's 3-4 defense for three years and many are questioning whether or not a change should be implemented to Miami's top ten defense. Miami has a few players that are suited to play in either defensive scheme, but also have some players that would find it hard to transition. 
The Dolphins have been able to maintain a top ten run defense while running the 3-4. The most important position in this scheme is the nose tackle since his main purpose is to plug the running lanes and take up blockers. The nose tackle should be a solid 6'6", 315 lbs to be able to command double teams. 
The Dolphins have a massive nose tackle in Paul Soliai, who will be a free agent this year and will probably demand too much money for the 'Fins to resign him. It would also cost way too much money to franchise him for the second year in a row. Other than Soliai, the Dolphins' only player that can really step up at nose tackle is Randy Starks, but his productivity at the 3-4 defensive end, or his ability to contribute more as a defensive tackle in a 4-3 will cause the Dolphins to hesitate before putting him in the middle. 
Without a big nose tackle, the 3-4 will not be as effective and will force the Dolphins to switch to a 4-3, whether they want to or not. 
As for the defensive tackle position in a 4-3, the Dolphins will be able to plug in Randy Starks and Jared Odrick at defensive tackle. Cameron Wake will be able to rush the passer on a consistent basis as a defensive end. The other defensive end position is up for grabs and might be filled through the draft with the possible selection of a Melvin Ingram (as proposed by Dolphins FC Scott Altman), or Quinton Coples in the first round.
Karlos Dansby fits the mold of a 4-3 Mike linebacker with his smarts and athleticism. On the other hand, Kevin Burnett and Koa Misi are the guys that would play the Sam and Will positions, as of right now. Burnett is a better coverage linebacker than he is rushing the passer, and the same goes for Misi. Burnett will most likely be utilized as the Will linebacker, forcing him to cover the tight end and running back while Misi will be used as a Sam linebacker allowing him to blitz more often and defend against screens.
As far as run defense, the 4-3 doesn't put as much pressure on the defensive tackles to read the play and fill the gap where he thinks the running back will run through. This provides the defensive linemen with more freedom to rush the passer. Since there will be more men inside the box, both defensive ends will be able to fill the C gap while the defensive tackles fill one A gap and one B gap. The Will will then take the other B gap while the Mike will take the A gap, and the Sam will take the D gap.
Expect the Dolphins to run a hybrid defense with the base being a 4-3. If the Dolphins are able to find a pure pass rusher through free agency or the draft, the 4-3 defense will be successful with the players they already have. They are a pass rusher away from having one of the most feared defensive fronts in the league, and adding a safety will give them the ability to be a consistent top defense for years to come.