I would say definitely teak for outdoors in the tropical climate. Wicker would be fine if it's in a covered area. Here is an article about different woods for tropical climates.

"The price of sustainably grown tropical outdoor furniture is becoming more and more affordable as the industry utilizes other varieties of sustainably grown tropical hardwoods, such as the following:

• Eucalyptus is a sustainably harvested plantation grown hardwood that possesses a smooth finish, lovely grain and a rich honey-red color that weathers beautifully due to the high oil content of its wood, and it smells good to boot. If allowed to weather naturally, the wood will take on a pleasing soft gray patina. It can be stained to retain the rich golden red color of the wood, however most people prefer the soft gray patina. Eucalyptus is less expensive and much easier to maintain than some of the other woods used for outdoor furniture.
• Balau is also one of the hardest of all tropical hardwoods. It is much more dense than teak and is in abundant supply. Like eucalyptus, it is more affordable than teak and will also withstand years and years of exposure to the elements. You will want to treat the wood occasionally with good wood oil if you wish to preserve the natural color, however this is a very low maintenance outdoor wood.
• Teak for good reason has become one of the most sought after of all the tropical hardwoods. Although it was at one time the preferred hardwood, along with mahogany, for ship building and decking, it is now grown on teak plantations due to its scarcity. The demand for teak is still high among those who are able to make the investment in furniture made from this beautiful top quality wood. Teak outdoor furniture is one of the more expensive options for outdoor furniture." http://www.thehouseandhomemagazine.com/Articles/Vol1No8/OutdoorFurniture/tabid/228/Default.aspx

I back Phoebe as far as teak furniture is concerned. In our previous house we had teak flooring which was very good and it was low maintenance. So I am sure, teak will be great for outdoors too. I came across this article. It should clear your doubts.

http://thebasicwoodworking.com/which-is-the-best-wood-for-outdoor-furniture/

I love wicker personally as patio furniture, but I think it would be very difficult for you to maintain it, especially if you are living in tropical area.

Teak can look great on a patio! I'd recommend purchasing through someone with a great reputation and warranty like Janus et Cie. It's a bit pricier than other vendors but they stand by their product which is great. Good luck! :)

A good quality teak is always recommended for outdoor furniture. Here are few examples - http://warisan.com/group/outdoor.

These teak comes from a tropical climate and done many projects based on tropical design. So very good for tropical climate. http://warisan.com/projects