They are really like apples and oranges. RO water is water that has been passed through a membrane under high pressure. The pores in the membrane are so small that only pure water can pass through and bigger particles like lead and silicates are left behind. It is like an extremely fine filter.
DI water is water that has passed through a DI reaction chamber. Here, dissolved particles in the water are chemically removed through a process called deionization. For example, when something like sugar dissolves in a glass of water, the sugar becomes electrically or ionically attached to the water molecules. Simple RO filtering can not remove many ionically dissolved substances. But because DI'ing is a chemical process, DI'ing water cannot remove many of the non ionically dissolved particles.
If you could only chose one or the other, I would chose RO water. Most of the contaminates in water are free floating anyway and using a RO filter will generally give you the cleanest water (over just plain DI water).
If you want the best water you can get, you need water that has been both RO filtered and DI treated. Here you remove all free floating/suspended particles and all ionically disolved substances.
DI water has no chlorine (dissolves ionically) and RO water has no copper (retained in a suspension)... You need both to have good water.