Q: Which one is more effective? Chemical peel or laser? 
A: Both chemical peel (using fruit acid or chemical acid) and laser resurfacing are meant to remove the top most layer of the skin to reveal a better quality skin beneath.
Laser treatment is by default more precise as compare to chemical peel. Be it the dept of laser penetration, the intensity of laser or other parameters are adjustable and predictable, i.e. just a button away.
Whereas for chemical peel, we can’t quantitatively adjust its dept of penetration or intensity. For instance, if there is an open wound (a burst acne) or injury to the skin, the acid will penetrate the skin deeper and the effect more intense and may easily cause a burn.
People with sensitive skin cannot go for chemical peel but they can usually tolerate laser quite well.
The effects of laser treatment typically last longer than chemical peel. It also has an extra benefit as it can stimulate more collagen production due to the laser heat.
While a chemical peel may lessen fine lines and rough skin, the treatment won’t do as much good with deep wrinkles or sagging skin.
Although both can treat fine lines and wrinkles, lines around the eyes and vertical lines on the upper lips respond better to laser treatment.
If you want to achieve the same intensity of laser by using chemical peel, you may need to use a stronger acid which will cause more complications as compare to the same intensity of the laser treatment.
The only down side of laser compare to chemical peel is its pricing. Laser usually cost more than chemical peel.
Hope this will clarify some of your doubts. 
Dr. Tan
