What different Stack Exchange apps are available for the iPad?
I have used 2 for iPhone, and have eventually gone back to the Mobile View as it was considerably better than either:

Six-to-Eight: Free. Worked OK, but you can't actually log in, you can merely track yourself as a user without being able to actually do anything

StackMate: $.99. Looked great, but soon worked out that by Stack Exchange it actually meant just SO, and not the SE network - wasted dollar.

As for iPad, there are only 2 available that work on iPad:


Answers for Stack Exchange
FullStack


And they both suck (imho).

For a start, FullStack only supports the Trilogy sites and Ask Ubuntu, so not the whole network.  And while "Answers for" covers all sites, it shares a further letdown with Fullstack in that neither of them allow you to actually log in and do anything other than browse.  This (as per the comments) may be because the API calls do not allow posting, but there is no reason why an App developer cannot use the APIs where they are available, and also put in a normal HTML webview of the actual site to finish of the missing parts - using the API does not limit you to only using the API if you are writing an app.

The mobile web view is far superior in every respect unless you are looking for non interactive bedtime reading.  One noted problem with the mobile view is that Chat does not seem to recognise the fact that you are logged in, meaning that while transcripts are available, you cannot enter a room and participate.

In addition to the above, a quick hunt about StackApps yeilds the following results, which are either deprecated, or were never fully released and may be interesting to read up on.:


StackUp
Stack Reader
iStack


If you are wanting a native iOS app for reasons such as getting push notifications, you can easily bodge up a system for allowing push notifications for your inbox to be sent to you iOS device.  You will need the following:


An account with IFTTT
An account with Boxcar
Your Boxcar account linked into IFTTT
A task within IFTTT that says IF RSS - New feed item from  apple.stackexchange.com/feeds/user/9495/responses (change to your own user ID) THEN Boxcar - Send a message to my inbox
The Boxcar app downloaded and installed on your iOS device.


Then, whenever you get a notification (an answer to your question, a comment on your answer, a shout in Chat etc) in your SE global inbox, it will send you a message into Boxcar, that may look something approaching the following:



You can customise the wording in the notification,but I have stuck to the defaults in this example.  Note, that the IFTTT feed checks currently run every 15 minutes.