If you use pushViewController you will automatically get a "Back" button in the navigation bar. If you use presentModalViewController you do not, and generally will have to implement your own controls and/or callbacks to handle dismissing the controller.
Conceptually the modal presentation style is generally used for atomic tasks that you cannot navigate away from (i.e. you either complete the task, or you cancel, and you cannot do anything else within the app until you do one or the other).
If you're wondering why have the difference in the first place, I can't say. Personally I think frameworks that provide a unified API for moving from one controller to another (like cocos2d, or Android) make a lot more sense.
You use modal view controllers to focus the user's attention on a Task. When you push, the user is in some kind of navigation flow, but still has the total application at their fingertips. They might decide to go forward or backward, switch to a different tab in the middle, whatever. When they get a modal view controller, they can't do any of that until the task is completed or canceled out of (the modal view is dismissed)
When you present a modal view controller, the system creates a parent-child relationship between the view controller that did the presenting and the view controller that was presented. Specifically, the view controller that did the presenting updates its modalViewController property to point to its presented (child) view controller. Similarly, the presented view controller updates its parentViewController property to point back to the view controller that presented it.
Modal view controllers provide interesting ways to manage the flow of your application. Most commonly, applications use modal view controllers as a temporary interruption in order to obtain key information from the user. However, you can also use modally presented view controllers to implement alternate interfaces for your application at specific times.
So, from my understanding this one is best option.
[self.navigationController pushViewController:view animated:YES];