I hope you enjoy them.
You can find a client that suites your needs on ADNCC which enables you to select features and operating systems to give you all clients that match the selected values.
Now for some short reviews for several clients.
FYI the clients on my homescreen are Felix, hAppy, Patter and Sprinter.
Have a look at http://adncc.nigma.de by @chemiker based on the client feature matrix by me to find a client that suites your needs.
Alphred: A workflow for Alfred2, the popular launcher on OS X. It allows to send a post or a pm right from Alfred incl. link entities. One of my favorite ways to do a post or reply to a private message from my main account.
Chapper: The only client I use on Win7. Support for Patter included. Feels cramped but in an upcoming update is theming support which enables me to set it up in a comfortable way. Good,could be better, previews from the upcoming update look very promising.
Chimp: Feature-rich, even with support for public Patter-rooms and it has push. An interesting UI-concept, which you might know from Path. Lots of information on the posts & can feel a bit cramped. Feels a bit slow. Nice client with a lot of potential.
Climber: The point & take a short video of app.net. 11 seconds have to be enough. Clean and fast interface, also support for the Places-API to set your location. Don’t forget to set the #Climber-hashtag.
Felix: Feature-rich and a good experience with a full-screen mode. Now also with support for multiple accounts and a dark theme. Has a clever implementation of link entities. To top it off it gets all the time updates. I use it all the time.
hAppy: Probably the feature-richest client. Sadly no push. Multiple account-support, link entities, a dark theme and the best client when your connection is slow. Also Complete Patter-support. Could I install only 1 client on my iPhone, this would be it.
Kiwi: A good client for Mac OS X. The only OS X-client with support for private messages. Regrettably no support for link entities or multiple accounts. My main client on OS X.
Netbot (iPhone / iPad): Feature-rich and some clever ideas, especially its support for “repost from” when you want to repost a post from another account. There’s also a good search.
It has push, but not for PMs.
Looks exactly like Tweetbot. For experiencing app.net like Twitter that might be the client of you choice.
Patter: The cleanest experience for chatting in Patter-channels. It supports PM and all features of Patter, incl. broadcasting. Otherwise features are missing like push or copying URLs etc but those are in development. Just for chatting it is great.
Riposte: A clean interface, with a good UI streamlined to be used with only one hand. Push, multiple accounts, dark theme, pictures are shown completely inline and it is really fast. Regrettably it has no support for link entities. But it is free.
Sail: A client that allows me to send a post fast on OS X with link entities to any of my accounts. Just a window, write a post, select your account, send. That’s it. Clean and quick.
Screenfeeder: Have several social feeds? Having your iPhone or iPad lying next to you or somewhere very present? Screenfeeder will show those feeds post by post to you. Your own neatly designed app.net-wall so to say.
Spoonbill: One of the first clients for the iPhone. The only client that supports an alternative but real threading-view for threads. Just for that it is worth a look. Featurewise there is not so much to say and feels a bit overdesigned.
Sprinter: The point & shoot of app.net. Open the app, make a photo, apply a filter, write your post, don’t forget to add the #Sprinter-hashtag, add a location based on the Places-API and send it out. Clean & fast. But it feels like something is missing.
Stream: Stream is clean and looks very polished, reminds me a bit on the old Tweetie for the iPhone. It has push, no link entities, no support for private messages. Needs to work on its features and could become a very good client.
Wedge: A good client for OS X that I use for my secondary account. Unfortunately no private messages but a nice interactions-view. Sadly it seems that it is not in development anymore. It was the first real good client for OS X.