Both a Roth IRA and a 529 plan allow you to invest money that you do not have to pay taxes on upon withdrawal -- the money the investment makes can be used tax-free.
Traditional IRAs function in the reverse -- you don't pay taxes on the money you put in (presuming you're under the income limit), but you do pay taxes on the money that you take out.
Traditional and Roth IRAs share a total $5,500 contribution limit per year, which limits the opportunity to use a Traditional IRA in addition to a Roth IRA.
For the Roth IRA vs the 529, they are similar in their tax structure.
The advantage the Roth brings to the table is its flexibility. It is easier to withdraw the money (you can always withdraw for educational expenses, but you can withdraw your original contributions at any time with no penalty, for any reason). Unused money in a Roth IRA can still be saved for retirement.
The advantage of the 529 plan is that it has no contribution limit, unlike a Roth IRA, which has a contribution limit of $5,500 per year. In addition, there may be state-by-state tax benefits. However, if you withdraw money from the 529 plan for anything besides educational expenses, you will pay a penalty.