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.
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.
Moog Filtatron is a realtime audio filter and effects engine. Import any song on your iDevice into the Sampler, run a sound through a virtual version of the famous Moog filter with a little (or a lot) of filter modulation, delay, and overdrive to create your own musical statement. Support for multi-touch X-Y pads provide highly tweakable performance control for live use.