I think you can use both in slightly different situations. You need to add to word "a" to the sentence. "The soldiers wear a distinctive uniform". I think this is the better of the 2 sentences. That means it's unique or it stands out. "Distinct is also correct, but only if you are comparing it to another uniform.

Hello Ruby, "distinctive" means serving to distinguish and identify a specie or a group,while "distinct" means recognized,marked or or constituting a separate entity . Here "distinctive " uniforms is more appropriate to use, because if you used "distinct" it might mean that their uniforms are not alike, each of them is wearing a different suit in quality or shape. If you don't add a definite article "a" to the sentence you can put "uniform" in the plural . "The soldiers wear distinctive (distinct) uniforms."