Hi,
A midi controller only sends out midi data. If you exsperience an audio issue when using a Keylab and not when using a Alesis controller, then it's because the midi values send out from the 2 controllers is'nt the same. There can be different reasons for this like how velocity and aftertouch works and respond on the 2 controllers.
I don't know what you mean by the sound "break up". But the distortion can be because an output level is set to high, or something else is getting a too high input level. This can be anywhere in the audio chain.
If in example your Alesis controller does'nt have aftertouch like the Keylab MK2 has, then perhaps it even can be about a CPU overload/ latency issues, if aftertouch messages actually affect your instrument to use more CPU ressources. Or perhaps you have different velocity curves or sensisivity on the two controllers. But there is nothing wrong in any of this.
I suggest you check your audio chain to see if anything is over 0 db and if so adjust that. Also check that a CPU core is'nt overloaded and if so adjust the soundcard settings or other settings, that you might have for this.
I assume the velocity and aftertouch does work on your controller, as you don't mention anything about that.