Amplified live music can overpower a digital field recorder if the levels are too high, but with the addition of a compressor/limiter you can make a balanced, clear recording.
A digital field recorder will capture a warm range of acoustic dynamics. The condenser microphones are constructed for subtleties in tone.
High-end field recorders consist of two built-in condenser microphones which boost quieter sounds. In an amplified venue it will even capture a spectrum of crowd noise.
Mono digital field recorders have one microphone and will condense all sound into one audio track. Smaller venues and rooms with less people are good for mono.
The best live sound you can get is by connecting your digital recorder directly into the sound board. These recordings are of the highest quality, and this is what bands sell when they put out a live album.