Each has advantages and disadvantages. If you keep the money in your name, either in accounts specifically earmarked for college or as a part of a general family portfolio, it will be subject to your level of taxation but you will retain control over the money.
If the assets are in the student’s name, the earnings income likely will be taxed at a lower rate. Often a custodial account is used, under either the Uniform Gifts to Minors Act (UGMA) or the Uniform Transfers to Minors Act (UTMA). However, if you put the money in your child’s name, he or she gains control over it on turning 18.
In certain situations, usually involving wealthy families, specialized types of trusts may be a good option.