A. You face two questions here - 1) should you sell the stocks and give your children cash, or give them the stocks and let them sell; 2) which account should you use.
Assume you have owned those stocks for more than 1 year, and you are in a higher tax bracket than your children are, you are better off giving them stocks from your brokerage account, because -
a) If your IRA is a traditional IRA account, you would owe tax on the market value of the stock at the time of the transfer. If your IRA is Roth IRA, while the distribution is tax-free, you will lose the tax-free growth shelter from Roth.
b) By giving your children stocks rather than cash, they, not you, would owe the tax on the appreciation you have enjoyed. Since they are in lower tax brackets than you are, they will owe less in capital-gain tax than you would. For example, if they are in the 10%-15% tax bracket, they could pay 0% long term capital gain tax, even they don't wait a year to sell the stocks (because you have held the stocks for more than 1 year).