RDFS and SKOS can be easily used side by side, because their focus is somewhat different.
RDFS is something that directly emerges from the RDF data model and its serializations. It starts with the RDF inference/entailment regime that models the most basic thing anyone could infer from a triple a b c – that b is a property, thus we need rdf:type and rdf:Property to express that fact (that's why those two are not in rdfs:). One step further, we have RDFS that again starts at rdf:type (making its range a class) and rdf:Property (inferring it is a class, and allowing describing subproperties). Then we have OWL that allows even greated degree of inference, but also makes it possible to detect (or create) contradictions.
RDFS is focused on inference; all of its classes and properties are centered around it: rdfs:domain and rdfs:range are defined in terms of inference of rdf:type; rdfs:subClassOf and rdfs:subPropertyOf are defined in terms of inference of arbitrary properties etc. Of course (along with OWL) one can also use it to describe a vocabulary itself, making it a sort of meta-RDF language (but, unlike OWL, it can describe itself).
RDFS is similar to classical object-oriented languages, but it also makes it possible to express classes of classes etc. There is also a difference between "being an instance of" (rdf:type) and "being a subclass of" (rdfs:subClassOf).
SKOS is oblivious to classes and properties as seen by RDF, as it stems from what we humans observe around us: we don't usually talk about a "class of cars", we talk about a car. Sets and classes are left to logicians and philosophers, and we are left with concepts. Concepts are the things we see around us, some apply to a broad range of things (a car, an electric car), some to just one thing (my neighbor's car). We don't need higher-order set theory to talk about them, and neither does SKOS, everything is described as an individual concept, some more general/abstract than others. Moreover, getting into higher orders is, in a sense, explicitly disallowed by SKOS by the rule that a concept is not a concept scheme.
SKOS may be set-theoretically limited but it is nonetheless powerful. Sometimes, it is easier to use it to talk about vague concepts (is "my neighbor's car" a class or an individual? SKOS doesn't care), sometimes it is necessary to describe concepts that don't fit in the RDFS hierarchy at all (related, close/exact match), not necessarily for computers to understand but definitely for humans.
SKOS's model reminds me of JavaScript, where you don't have traditional classes but use prototypes to express inheritance, similarly to skos:broader. In this regard, a class is an object and an object is a class; there is no difference between an instance and a subclass.
Hopefully you see now that the answer to whether to use one or the other is to use both, in their respective places. You use RDFS/OWL for vocabularies or inference, when you need strict definitions, and you use SKOS for concepts/taxonomies, when you need vague definitions, but there are places where both are perfectly usable.
