BIG OH specifies only an asymptotic upper bound, while BIG THETA species both the asymptotic upper and lower bound. It's usually more useful and easier to only worry about the worst case, and say that its run time or whatever is BIG OH of something. There may be certain classes of inputs for which the algorithm will have a smaller asymptotic run time, so in these cases, you wont be able to specify BIG THETA for general input.