I'm glad to see you over here asking these questions. I'll provide my perspective as a former master's level clinician:
If you take cost completely out of the equation and are just comparing training experiences, the advantages of a Psy.D. over master's level training is coursework in psychological testing, a somewhat stronger statistical background, and a little more content knowledge in the general practice of psychology. There is also the obvious factor of more hours in practicum and the year long internship. Provided that you're an absolutely stellar student, you might be able to overcome many of the limitations and biases about the institution that you've been accepted into and land a good APA accredited internship where you want to live. Note though that many Psy.Ds from unfunded institutions end up in jobs also occupied by master's level clinicians.
At the master's level, you generally have two options: the master's in social work (MSW) and the master's in counseling (MA/MS). In social work, psychotherapy is a speciality within the broader field of social work and thus much of your coursework will be focused on preparing you to be a social work (resource management, case management, policy, advocacy, and the like). There are programs where you can explicitly declare a clinical interest as a concentration. With the master's in counseling, the coursework is heavy on direct clinical work from a humanistic perspective, which I've heavily criticized in other threads. Both degrees will require one or two years of practicum. Both degrees will require a national exam and then 1-2 years of supervised post-master's experience prior to earning a state license.
Those who do well, from what I've observed, use that time to hone their skills in some kind of structured or semi-structured training experience like an institute or post-master's fellowship. These folks may also gain experience in a hospital or community mental health setting. The prevailing wisdom for clinicians is to pick a specialty, get training in it, and then offer that specific service. Doing actual good in the world would mean choosing a psychotherapy modality with some actual unbiased research behind it (hint...not EMDR). If you took a path where you got a master's degree and received specialized training in one area of practice, I would contend that your clinical work would be likely equal to, or likely superior to the training you would receive at an unfunded Psy.D. program (e.g.: an apprentice vs. a coursework model).
As far as reimbursement rates go, it widely depends on where you live. In some states, the reimbursement rates for psychotherapy codes are the same for all mental health practitioners. In others, psychologists make more (but not enough more to justify the debt of an unfunded Psy.D. program!). My master's level friends in private practice are well above the BLS average salary for their professions, but my psychologist friends do report higher income than my master's friends. There's distance between those two figures, but I'm not sure it's a statistically significant difference.