MIDI is for routing musical events (which you should be able to do with the Apple MIDI routing control panel) But as you say, what you need a program for routing Audio between the applications. The options I know of are:
Jack OS X:
http://www.jackosx.com/
Soundflower:
http://www.cycling74.com/products/soundflower
You might also be able to use wormhole, although this is usually used for routing audio between computers:
http://plasq.com/wormhole
If you have a multi-channel audio interface there's always the old stand-by: plug the output back into a spare input.
Comparing Logic to AudioMulch is a funny type of comparison to make (one is a DAW, one is a patchable performance audio processing and sound mangling environment). There will always be cases where one is better than the other. I recognise that tighter integration with DAWs is desirable for some uses and I'll be working on improving AudioMulch for this kind of use over the next year or so.
Hope that helps.
Ross Bencina
Maker of AudioMulch
P.S. Feel free to drop by the AudioMulch support forums if you have any other questions.