I think you have to consider each child's individual personality when making the decision on whether or not to skip.
I have 2 gifted children.
My eldest skipped 1st grade and was much happier. He is now in a 3rd grade gifted class and doing well overall. The work is not hard for him at all and he loves being challenged. However, he is not as good at listening/focusing as the older kids and gets tired quicker. Also, his fine motor skills are not as developed - this makes a big difference when trying to keep up with written activities.
My second child is also gifted - reading at fifth grade level in kindergarten. However, I would not dream of letting her skip a grade. She is not as mature or motivated and does not particularly like working! She does spend half the day in 1st grade for reading. The teacher there is great at working with kids of differing abilities and my plan is just to have my daughter spend next year with her full time.
Having gifted children is really hard work. You have to find teachers who are willing to be flexible and communicate frequently with you.
Good luck!