NSOperation* classes are the higher level api. They hide GCD's lower level api from you so that you can concentrate on getting the task done.
The rule of thumb is: Use the api of the highest level first and then degrade based on what you need to accomplish.
The advantage of this approach is that your code stays most agnostic to the specific implementation the vendor provides.
In this example, using NSOperation, you'll be using Apple's implementation of execution queueing (using GCD). Should Apple ever decide to change the details of implementation behind the scenes they can do so without breaking your application's code.
One such example would be Apple deprecating GCD and using a completely different library (which is unlikely because Apple created GCD and everybody seems to love it).
Regarding the matter i recommend consulting the following resources:
Now, regarding your specific questions:
What are the differences between dispatch_*() and NSOperationQueue, [...]
See above.
[...] and is there any reason (technical, performance, stylistic, or otherwise) that I should use one over the other?
If the NSOperation stuff gets your job done, use it.
Is NSOperationQueue just an Objective-C wrapper around dispatch_async, or is there more to it than that?
Yes, it basically is. Plus features like operation dependencies, easy start/stop.
Amendment
To say, use the highest level api first might sound intriguing. Of course, if you need a quick way to run code on a specific thread, you don't want to write a whole lot of boilerplate code which makes the use of lower level C functions perfectly valid:
dispatch_async(dispatch_get_main_queue(), ^{
do_something();
});
But consider this:
[[NSOperationQueue mainQueue] addOperationWithBlock:^{
do_something();
}];
I'd recommend the latter because most of what you'll write is Objective-C anyway so why not embrace its expressiveness?
NSOperationswhere you can manage functionality specific to that task properly. This is scalable and beautiful at the same time. – Boom