Running time for Breadth-First-Search vs Depth-First-Search
The running time of both BFS and DFS are $\Theta(V+E)$ since both of them are guaranteed to visit every vertex and every edge at least once. Note that we are talking about the situation when the input graph is a connected graph whose edges are given by adjacency-list, the most common situation (in the course of your study).

It is not surprising that the CLRS book presents the running time of BFS as $O(V+E)$ even though $\Theta(V+E)$ is the optimal asymptotic bound for its running time. It is actually a general practice that the running time of an algorithm is described in term of big $O$ even though it might be possible to describe in term of big $\Theta$. The reason is that how tight we can bound the  running time of an algorithm from above is the major concern for many situations.