I loved ASIHTTPRequest and I was sad to see it go. However, the developer of ASI was right, ASIHTTPRequest has become so large and bloated that even he couldn't devote time to bring it to par with newest features of iOS and other frameworks. I moved on and now use AFNetworking.
That said, I must say that AFNetworking is much more unstable than ASIHTTP, and for the things I use it for, it needs refinement.
I often need to make HTTP requests to 100 HTTP sources before I display my results on screen, and I have put AFHTTPNetworkOperation into an operation queue. Before all results are downloaded, I want to be able to cancel all operations inside the operation queue and then dismiss the view controller that holds the results.
That doesn't always work.
I get crashes at random times with AFNetworking, while with ASIHTTPRequest, this operations were working flawlessly. I wish I could say which specific part of AFNetworking is crashing, as it keeps crashing at different points (however, most of these times the debugger points to the NSRunLoop that creates an NSURLConnection object). So, AFNetworking needs to mature in order to be considered as complete as ASIHTTPRequest was.
Also, ASIHTTPRequests supports client authentication, which AFNetworking lacks at the moment. The only way to implement it is to subclass AFHTTPRequestOperation and to override NSURLConnection's authentication methods. However, if you start getting involved with NSURLConnection, you will notice that putting NSURLConnection inside an NSOperation wrapper and writing completion blocks isn't so hard as it sounds and you will start thinking what keeps you from dumping 3rd party libraries.
ASI uses a whole different approach, since it uses CFNetworking (lower-level foundation frameworks based on C) to make downloading and file uploading possible, skipping NSURLConnection completely, and touching concepts most of us OS X and iOS developers are too afraid to. Because of this, you get better file uploading and downloading, even web page caches.
Which do i prefer? It's hard to say. If AFNetworking matures enough, I will like it more than ASI. Until then, I can't help but admire ASI, and the way it became one of the most used frameworks of all time for OS X and iOS.
EDIT:
I think it's time to update this answer, as things have changed a bit after this post.
This post was written some time ago, and AFNetworking has matured enough. 1-2 months ago AF posted a small update for POST operations that was my last complaint about the framework (a small line ending fault was the reason that echonest uploads failed with AF but were completed fine with ASI). Authentication is not an issue with AFnetworking, as for complex authentication methods you can subclass the operation and make your own calls and AFHTTPClient makes basic authentication a piece of cake. By subclassing AFHTTPClient you can make an entire service consumer in little time.
Not to mention the absolutely necessary UIImage additions that AFNetworking offers. With blocks and custom completion blocks and some clever algorithm, you can make table views with asynchronous image downloading and cell filling pretty easily, whereas in ASI you had to make operation queues for bandwidth throttling and mind yourself to cancel and resume the operation queue according to table view visibility, and stuff like that. Development time of such operations has been halved.
I also love the success and failure blocks. ASI has only a completion block (which is actually the completion block of NSOperation). You had to check whether you had an error on completion and act accordingly. For complex web services, you could get lost in all the "ifs" and "elses"; In AFNetworking, things are much more simple and intuitive.
ASI was great for its time, but with AF you can change the way you handle web services completely in a good way, and make scalable applications more easily. I really believe that there is no reason whatsoever to stick with ASI anymore, unless you want to target iOS 3 and below.
