Did you know that Connector can not only send audio but also MIDI between applications? Here is an example, sending midi from Ableton Live to Pro Tools in real time.
This video explains in details how this can be done, and what you can use this trick for.
This is a helpful walkthrough of routing MIDI between DAWs without flattening the performance. Keeping the audio and MIDI stages separate makes the workflow much easier to troubleshoot when the detected notes are not quite right.