We have regularly made live recordings of band performances over the years. Recording on location and later the final mix done from our studio. We had invested in a double Alesis HD24 hard-disk recording set up especially for this sport.
The 2 connected machines were neatly in a flight case, together with the correct number of pre-amps. This set up was taken to the location of the concert and was linked to the stage set up on stage by means of a splitter. Microphones and DI boxes intended for the PA were given a double function in this way. It was a lot of work, but the result was good. The registration of the direct microphone signals was later unloaded in our studio into Protools for the final mix. Nowadays this is much easier. Most venues work FOH with digital tables, where you directly connect a laptop. Signals are leveled via the table's pre-amps and passed dry for recording. You only need to bring a hard drive to take the recordings to the studio for the mix.
This is actually a very effective and relatively cheap way to capture the magic of a band. For example, we were the founders of the rock band Voltage. We made live recordings at Music Center De Bosuil, which later recorded at Rock Inc. Recording are mixed.
Because the band had a good sound and played really tight, the mixing was a joy and a representative, honest and atmospheric live demo was created. If you choose this recording method, it is a must for the band to be well prepared on stage.