ARC is just play old retain/release (MRC) with the compiler figuring out when to call retain/release. It will tend to have higher performance, lower peak memory use, and more predictable performance than a GC system.
On the other hand some types of data structure are not possible with ARC (or MRC), while GC can handle them.
As an example, if you have a class named node, and node has an NSArray of children, and a single reference to its parent that "just works" with GC. With ARC (and manual reference counting as well) you have a problem. Any given node will be referenced from its children and also from its parent.
Like:
A -> [B1, B2, B3]
B1 -> A, B2 -> A, B3 -> A
All is fine while you are using A (say via a local variable).
When you are done with it (and B1/B2/B3), a GC system will eventually decide to look at everything it can find starting from the stack and CPU registers. It will never find A,B1,B2,B3 so it will finalize them and recycle the memory into other objects.
When you use ARC or MRC, and finish with A it have a refcount of 3 (B1, B2, and B3 all reference it), and B1/B2/B3 will all have a reference count of 1 (A's NSArray holds one reference to each). So all of those objects remain live even though nothing can ever use them.
The common solution is to decide one of those references needs to be weak (not contribute to the reference count). That will work for some usage patterns, for example if you reference B1/B2/B3 only via A. However in other patterns it fails. For example if you will sometimes hold onto B1, and expect to climb back up via the parent pointer and find A. With a weak reference if you only hold onto B1, A can (and normally will) evaporate, and take B2, and B3 with it.
Sometimes this isn't an issue, but some very useful and natural ways of working with complex structures of data are very difficult to use with ARC/MRC.
So ARC targets the same sort of problems GC targets. However ARC works on a more limited set of usage patterns then GC, so if you took a GC language (like Java) and grafted something like ARC onto it some programs wouldn't work any more (or at least would generate tons of abandoned memory, and may cause serious swapping issues or run out of memory or swap space).
You can also say ARC puts a bigger priority on performance (or maybe predictability) while GC puts a bigger priority on being a generic solution. As a result GC has less predictable CPU/memory demands, and a lower performance (normally) than ARC, but can handle any usage pattern. ARC will work much better for many many common usage patterns, but for a few (valid!) usage patterns it will fall over and die.