The iTunes MP3 encoder is faster than LAME on OS X, but iRecordMusic cannot use it for real-time encoding. iRecordMusic can use LAME for real-time encoding.

As for which encoder produces better quality MP3s, this is highly subjective and dependent upon individual listeners. In its favour, LAME is highly configurable, and has many preset encoding styles, such as 'r3mix' which is considered extremely good.