Is there a difference between mirtazapine and amitriptyline in terms of effectiveness for pain and sleep?

No direct answer. These are 2 different drugs. Again, there is "no better than" or "as good as". Treatment of any disorder should be individualized. I would think that Remeron (mirtazapine) is more often prescribed for sleep disorders where as Amitriptyline is more often prescribed for pain when talking about these 2 conditions specifically.