I'll share my experience and see if this helps you:
We bought some property.
Hired an architect and designed a home.
Spoke with and interviewed many builders.
Narrowed it down to 3, and asked all 3 to bid the plans.
In the end, we chose our builder based off his qualities, not cost-plus vs flat fee. And I would recommend the same.
Now that I'm 3 months into the build, I'm really really happy with our choice because I trust him, and I trust his right hand co-GC. They are in constant communication with me, always on site, walk the site with me, answer all my questions no matter how dumb they are. Its nice to lay my head down at night knowing the home we spent years designing will be built like I want it built.
So thats my recommendation. Forget how its priced. Choose the builder that you feel the best about AND has the communication style that fits your personality needs.
Ours happens to be cost-plus. I find it to be very fair. I knew up front what his +% was, I see every invoice, those all go to the bank for draws. There are differing opinions about the cost-plus method, but I'm very satisfied. That said, he could have been flat fee and I wouldn't have cared. That didn't factor into my decision, and I don't think it should. When your in the depths of building your house, you'll care WAY more about good comm, and way less about how he's getting paid.