There is a definite difference in taste and cooking characteristics. Turbinado sugar is simply dried raw pressed sugar cane. Brown sugar is white sugar with molasses added. Dark brown sugar simply has more molasses than light brown.
So, in order to answer your question about changing we need to know what the goal is. If you want more heat tolerance, and don't need the molasses flavor, switch. Just know that removing the brown sugar will indeed alter the flavor. Of course, you can keep the flavor by simply adding molasses, or (as I now prefer), you can simply replace both the sugar and the molasses with Steen's syrup
I hope this helps,