Lemur allows you to turn your device into a fully customizable MIDI control surface. Lemur has more features which makes it a lot more powerful than TouchOSC.
However, this functionality comes at the cost of complexity and makes Lemur harder to get started with. But if you want to make sure you have every single control option available, it is the most powerful control software you can have.
TouchOSC allows to remote control and receive feedback from software and hardware that implement the OSC or MIDI protocols such as Apple Logic Pro/Express, Ableton Live, Renoise, Pure Data, Max/MSP/Jitter, Max for Live, OSCulator, VDMX, Resolume Avenue/Arena, Modul8, Plogue Bidule, NI Traktor, NI Reaktor, Quartz Composer, Supercollider, vvvv, Derivative TouchDesigner, Isadora and many others.
iShred LIVE works with standard iOS guitar interfaces to bring killer effects and tools for your guitar! Just plug in and crank it up: the free iShred LIVE app puts you in control of an amp simulator with variable overdrive, and starts you with two free effects, the HK-2000 digital delay and Q-36 Space Modulator/Flanger, and a built-in noise gate and filter.
DJ Rig is a full-featured, double-deck DJ mixing app for iPhone. It provides instant song-playing from the device’s music library, automatic tempo sync and beat match, sample-based pads and performance recording, plus an arsenal of high-quality DJ effects.
When used with the new iRig MIX audio mixer for iOS devices, DJ Rig provides the most portable professional setup for mobile DJs and musicians.