Lye relaxers are more caustic because the PH is 14, like drano. People with sensitive scalps can not use lye relaxers. No lye relaxers have a lower PH, I believe it's around 11/12. Some have a PH of 9, but these are not really effective at straighting very curly/coarse hair. That's still high, but less damaging than lye. I read at FDA.gov that the best no lye relaxer tested was TCB's bone straight. Less damageing, less drying.
I think the only problem with no lye is the calcium that can build up. But, if you rinse really, really, really, really, good you shouldn't have a problem, at least I didn't. I'm natural now, but when I did relax I used mostly no lye. When I'd go to the salon, my stylist would use lye. I do remember my hair being dry, but it was dry whether I used lye or no lye. Plus, I didn't know how to care for my hair properly.
If I were to ever relax my hair again, I will definatly use no lye. Because in my experience no lye relaxers didn't burn my scalp or make my hair look "chewed up" like the lye relaxers.
Correction: My info was taken from the fda AND consumer reports.