In general:
A lye relaxer is better for the hair than a no-lye in that it is less drying to the hair. However, a lye relaxer is harsher on the scalp which is why it is imperative to base the scalp before applying a lye relaxer.
The no-lye relaxer is better for those with an utterly sensitive scalp, but is drying to the hair.
Many on the board (including me) have had issues getting the hair straight with lye relaxers. I have found with experimentation that it may need to be left longer and it may need more "help" straightening the hair. This can be accomplished mechanically with the help of the back of your rattail comb when smoothing the relaxer. I also smooth with the teeth of the rattail comb, which is usually said to be a big no-no. But everyone's hair is different and my hair is somewhat resistant to lye relaxers, but I refuse to use a no-lye ever since I was educated on the difference between the lye and no-lye. My hair has thrived so much more since switching from a no-lye to a lye relaxer in 2000.