It would be impossible to list out every single pro and con and then decide whether there are more pros and cons. Also, some factors may be more important to you so there are several things you should consider before making an informed opinion. I will answer your first question, and list out potential advantages, although this will not be an exhaustive list.
The most obvious advantage for "designer babies", or being able to select for certain traits in offspring, would be for medical purposes. Certain diseases, like Down's syndrome or cystic fibrosis, can be prevented by selecting for embryos that do not carry the mutation. There is also a lot of evidence now that certain genes predispose for certain diseases, such as cardiovascular diseases or cancer. These diseases can potentially be eliminated, or at least reduced, through designer babies.
Another advantage, although this is a more ethically ambiguous topic, is being able to select for non-medically related traits. For example, parents would be able to choose the sex, hair color, eye color, etc of their child. Even though genetics does not dictate all of our traits (nurture, or environment also plays an important role), this would in theory allow parents to pre-determine what their child will look or behave like, to some extent.
There are many ethical questions to consider when you are trying to decide whether you are for or against this issue. For example, should parents be allowed to select for traits of their child? Most people would not have a problem against selecting for healthy children, but where do you draw the line whether something is necessary or just desirable? What does this mean for parents who are unable to afford to "design" their babies? What will a society of "designed" and "normal" children be like?
In short, the technology behind designer babies has huge potential to eliminate or reduce many diseases, but the ethical issues and regulation around the use of this technology remains controversial.