Whether the tyre is tubed or tubeless mainly dictated by the construction of the wheel rims in the first place, the tyre itself in the second and the nature of the riding you do. Naturally, rims with wire spokes that go right through the middle of the rim need tubes while alloy rims that are cast as a single unit can accept tubeless tyres. Rims with spokes that attach to the rim on the side rather than the middle, can be used with or without tubes.
Tubed tyres and their associated spokes rims are hardier e.g. one can deflate the tyre to a greater extent when travelling over thick desert sand. They can also tackle tough off road conditions with stones, rocks and potholes as the spokes wheels can handle this type of abuse better than alloy wheels.
Tubed tyres are seldom speed rated over 200km per hour as they generate more heat than their tubeless counterparts. In the event of a sudden puncture they are also more dangerous as the tyre can easily come adrift from the rim (unlike tubeless).
Tubeless tyres and their light alloy rims are not well suited to tough conditions as they loose their shape and the tubeless tyres can no longer seal themselves against the rim. One of the big advantages of tubeless tyres is the ease of repair when one has a puncture as the tyre can stay on the rim during the repair process (large side wall punctures are the exception). They are also safer at high speeds and can be speed rated in excess of 300km per hour. The tyre also fits more tightly onto the rim meaning that a sudden puncture is less of a threat (this is why “breaking the bead” is more difficult than tubed tyres). Badly damaged tubeless tyres can accept a tube in an emergency if they are ridden slowly back to a repair shop.