Honestly, I would say the gentle sulfate. I've had my hair stripped by most non-sulfate poos I've tried, even ones that are supposed to be "organic" gentle enough for young children (e.g., Earth Friendly).

My hair usually takes several days of judicious moisturizing to recover. In contrast, however, a couple weeks ago I used TIGI Oatmeal & HOney shampoo for the first time. It has sulfates, but IIRC not too high up in the list and plenty of conditioners. My hair actually felt better than with conditioner only (well, it would since I had a lot of buildup and needed to clarify), and I needed a much smaller amount of conditioner once I'd shampooed than I usually need with co-washing.

But given the fact that most sulfates clean by weathering the hair shaft and can damage the follicles, too. I would rather use such shampoos at a max of twice a year, and try to find some non sulfate cleansers to use every month or so. At the moment I'm interested in trying aritha or Giovanni 50:50 shampoo.