It would depend on whether you plan to use the furniture outside or under the protection of a roof. Theoretically, both water and oil-based products could be used.
For example, you could "antique" wicker with thinned Gel Stain to pop up the color depth on an aging piece of natural wicker. However, Gel Stain is not exterior-rated and is very thick, making it cumbersome to apply and wipe off on a highly textured surface such as wicker.
In general, we would recommend using water-based finishes on wicker because they can be spayed.