The Boss BR1600CDR is also another option, I've been using one for approx 18 months and find the machine to be very compact, a lot of features, effects such as reverb (plate, hall) compressor, equalizer giving you the option of peak and shelving types, chorus/delay, drum patterns that are pre-set or programmable to suit your particular needs, guitar amp modelling, speaker modelling, bass simulator, vocal tools eg pitch correction, applied harmonies, relatively accurate constant loudness in the panning controls, flanger.
All the above effects and tools have a relatively wide range of options allowing the user to model and shape as desired.
Guitars, bass, keyboards can be recorded direct into the desk, the inbuilt amp modelling can produce some very realistic tones without the added process of miking up cabinets, eliminating outside unwanted noises etc.
The onboard Mastering tool can be very useful in giving that final polish to your recordings with tools such as enhancers, compression, equalizer etc.
A normalizing function is also onboard to achieve levelling on recorded tracks, the editing, track cut and erase is a very precise and easy tool to use.
Each track has a total of 16 virtual tracks, allowing the user to pick and choose the best performances for bounce down and mastering etc, effectively giving you a total of 256 tracks available for recording to.
Looping of tracks is available.
Scene setting allows you to set different eq settings, effects and volumes during playback of the tracks.
Onboard CD burner, also allowing playback of commercial CD's and importing samples etc.
USB connection for PC connection, midi, digital connections for monitors etc.
The list goes on, the machine has a few set backs, eg slow to load previously recorded songs, things I have learnt to live with for what it allows me to do.
Overall I find a very compact and versatile unit, I can't speak for the Korgs or Yamaha ( I do own Yamaha MD4).
Just a general rundown of the Boss, you may choose to give it a look in!
