Set relationship between Big-Oh and Theta notations
In general, a proposition $P$ is said to be stronger than $Q$ if $P$ implies $Q$ ( symbolically, $P\Rightarrow Q$)  and $NOT$( $Q$ implies $P$).  In the example at hand, $f \in \Theta(g) \Rightarrow f \in \mathcal{O}(g)$ , so that $f \in \Theta(g)$ is a stronger assertion than $f \in \mathcal{O}(g)$.