If you tried Dark Fired Kentucky blends, then that is a burley. I mean, Virginias can be fire-cured too, but DFK is generally burley tobacco.
Burley is not as sweet as Virginias; they tend to have a more earthy, woodsy, and occasionally chocolatey flavor. Most burleys tend to be air-cured, but they can come in many varieties and be processed by any multitude of methods.
Burley is generally considered to be well-suited to taking on the flavors of toppings and casings alike, and is often mixed in with blends to help provide body and balance.
I think how much a person can like burley-forward blends on their own is dependent on what their general tastes are. Burleys don't have much sugar on their own, so aside from aromatics, most burleys are going to have a more bitter and subdued flavor profile when compared with virginias. Because of this, unlike virginias, nearly all burley blends contain at least some other kind of tobacco in them, whether it be virginias, latakia, etc.
If you want a blend that is sweeter but still has a very burley forward approach, then something like Pegasus could fit the bill. If you enjoy those DFK blends, then something like Jupiter or Irish Flake may be worth trying.