Comparing two algorithms for all-pairs shortest paths
There is no standard definition for sparse graphs. Some common definition include graphs in which $E = o(V^2)$, $E=O(V^{2-\epsilon})$, $E = O(V^{1+\epsilon})$, $E=O(V^{1+o(1)})$, $E = O(V\log^C V)$, and $E = O(V)$.
In most situations, it is safe to assume that the graph is connected, and so $E \geq V-1$. In such cases, $VE + V^2\log V = O(V^2 E)$, and so an upper bound on the running time of the form $O(VE + V^2\log V)$ is better than an upper bound of the form $O(V^2 E)$: indeed, the former implies the latter.