See here for an explanation of the difference:
http://www.savingforcollege.com/articles/five-things-to-know-about-529s-and-financial-aid?page=2Personally I would choose the individual 529 over the custodial 529, because I want to retain control of those college savings assets longer than the custodial 529 set up and I want the option of moving money between my kids' accounts as needed in case one kid goes to a more expensive college or takes longer or whatever.
UTMAs and 529s are two completely different kinds of accounts and have completely different rules. I'm fairly certain you can transfer stocks in-kind to a UTMA but you cannot do so into a 529.
The ability to have lower taxes on the gains is pretty limited these days due to something called the "kiddie tax". Basically, high-income people figured out a while ago that their kids were in a lower tax bracket, so they would give appreciated stock to their kid, the kid would sell the stock, and then the kid would pay taxes on the capital gains at their lower rate. The IRS and Congress noticed people doing this, and so they changed the tax laws. Nowadays, in that scenario, a small amount of the capital gain can be paid at the kids rate, but if it's more than a few thousand dollars and the kid is under 18, the excess gets taxed at the parents' rate.