Lets say we are trying to solve some algorithmic problem $A$ that is dependent on input of size $n$. We say algorithm $B$ that runs in time $T(n)$, is asymptotically better than algorithm $C$ which runs in time $G(n)$ if we have: $G(n) = O(T(n))$, but $T(n)$ is not $O(G(n))$.
My question is related to the asymptotic running time of graph algorithms, which is usually dependent on $|V|$ and $|E|$. Specifically I want to focus on Prim's algorithm. If we implement the priority queue with a binary heap the run-time would be $O(E\log V)$. With Fibonacci heap we could get a run-time of $O(V\log V + E)$.
My question is do we say that $O(V\log V + E)$ is asymptotically better than $O(E\log V)$?
Let me clarify: I know that if the graph is dense the answer is yes. But if $E=O(V)$ both of the solutions are the same. I am more interested in what is usually defined as an asymptotic improvement in the case we have more than one variable, and even worse - the variables are not independent ($V-1\le E<V^2$, since we assume the graph is connected for Prim's algorithm).