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RO forces water through a super fine membrane as a filter for particles (and some chemicals). The two or three prefilters you see on the units remove larger particulates and some chemicals (usually a paper and carbon combination) and extend the life of the RO membrane.
DI is a resin that binds with (thus removing) metals.
If you have to chose between the two and can filter your water for particulates and chlorine (and anything else our providers add to keep bacteria minimized) then at least do a DI canister. As CaptFish mentions, a lot depends upon your water source but I switched to RO/DI water (from filtered tap) long before octopuses and noticed a big difference in the health of my tanks.
I saw this video of this guy comparing tap, RO/DI, and conditioned water with a TDS meter. The tap had a level of 140, the RO/DI had a level of 2, and the conditioned had a TDS of 200! Would this change what you said?
I am not sure what you mean by "conditioned". Some DI resins (combined with their filter chamber design) will put "sand" in the water (small resin particles that pass through the filter) that would show up on a TDS meter. At one time DI water was not considered potable (safe for drinking) but I have read this has changed. I am not sure if it is because the resins are trapped better, are larger grained or the original failure to meet drinking standards was in error. I keep an in-line TDS meter that I check from time to time (to see if I need to replace the RO membrane) and my post DI water is about the same as the water that has not entered the DI filter (I have a spigot that draws from a holding tank that has not been through the DI canister). You will see some RO/DI sellers note that "their" resins do not add detectable particulates. If this was the test the video was "exposing", see if you can find a year or if he posts anything about the type of resin he used.
As an aside, I have also started using a UV light in my freshwater holding bucket. There are pros and cons (all anecdotal) about using UV in a tank/sump but using one on RO/DI water before it is put in the tank can not be harmful. With the amount of mud I get in my water, I feel that it is hard not to expect bacteria in spite of the chemicals and removing the chemical is likely to allow surviving bacteria to grow.
I am sold on using RO/DI because of the observed difference in the health of my tanks pre-octo keeping BUT the water you start with DOES make a difference. Most "city" water is loaded with additives to keep bacteria at safe levels. Unlike our aquarium inhabitants, we can tolerate an amount of chlorine/chloramine but more and more people are filtering it out for drinking.