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Sole disadvantages?
Deionization only filters ions, so it can be 'blind' to other contaminants. It also can get microbiological contamination since bacteria and fungi can grow in the ion-exchange resins.
For reverse osmosis I guess the biggest issue is it's yield as you may have to use up to 4L of potable water to obtain 1L of purified water. It also may be much more expensive than a deionizator.