It's really hard to say anything that can be certain until you meet them both and get to draw your own conclusions, unfortunately. I highly agree with the suggestion of finding out about their experience with c-ptsd. That can be the biggest game changer in the quality of care you receive and it's sustainable effectiveness.
I was advised of two psychiatrists who gladly accepted my insurance at the time in my local area who were both highly recommended and sought after by others, yet neither one helped me. They further complicated my issues and helped me learn more of my inability to function healthily and feel at peace under the influence of most of their medications being prescribed. I wasn't a very strong self-advocate at that point in my life, still strongly believed in the power of meds and the mental health arena as I was also employed in the same scene, so I didn't speak out much when things didn't feel right, I just chose to move along when I was made to feel worse than when I arrived.
One spent a total of 15-20 minutes with me, making eye contact only once as I entered his office, declaring me severely depressed after only a few questions and glancing over the hard copy I gave him of definite issues I wished to address, ignored all of the trauma incidents and direct questions I asked, prescribed effexor, and said call him if I had any complications or if I felt I need another appt. Like he expected it to be a one-stop shop. I chose not to take it after already having some bad experiences with several other types of anti-depressants my doctor had prescribed. Knowing how long it takes to try it and then the time it takes to slowly come off of them, feeling the shittiest I had felt up until that point, thanks to my body's reactions to previously being a guinea pig was all I needed to decide to kick him to the curb.
The other one spent over 3 hours with me, which initially made me feel better about his attention to detail, asking tons of multiple choice questions he was entering into his computer, but he also blatantly ignored and never again mentioned the list of multiple traumatic incidents I supplied him with in writing (childhood sexual and physical abuse, teen rape, multiple domestic violence incidents with life-threats, workplace bullying), diagnosed me with severe adhd, severe depression, severe anxiety, and some kind of personality disorder that he just couldn't quite put his finger on (I was thinking, damn, does that mean I'll soon have one named after me??!!)...sent me home with an anti-depressant, some xanax, a stimulant at the highest dose, and 4 or 5 vitamin and mineral supplements. I thought I was gonna have to scrape my ass off the ceiling after taking all he recommended. His solution was for me to open the stimulant capsules in the future and dose out smaller portions of the powder. I gave him a few more chances, especially after hearing so many good things from others about his level of care, but he was strictly all about the meds and less about the roots of the issues. Needless to say, I never returned to either one, nor did I find a medication that soothed anything long-term in my highly sensitive being.
Not trying to plant fear, just trying to show a couple examples of how even the most highly recommended and sought after professionals can be as equally problematic as they can be perceived as being helpful. One person's life jacket can easily be another person's sinking ship, I guess is what I'm trying to say. It's pretty much a crap shoot no matter which direction you go. May you be able to research and find one who can genuinely recognize and address the roots of the trauma issues while actually helping and bringing you some long sought after relief and peace of mind.