A huge piece of the puzzle that is missing so far in this thread is the hormonal response to different types of exercise.
In addition to the hormonal response you have the upregulation of transcription for the GLUT (glucose transport factors), which HIIT is better at.
In my experience low intensity cardio has the benefit of not pushing me into overtraining. HIIT should be treated like a weight lifting session to maximize the aforementioned processes above, and at least for me should be at least 8 hours away from a lifting session. Low intensity can be done in conjunction with lifting.
Do both, but at the right times and for the right reasons.