Vertex Cover can be easily reduced to Independent Set and vice versa.However, in the context of parameterized complexity, Independent set is harder than Vertex Cover. A kernel with $2k$ vertices exists for Vertex Cover, but Independent Set is W1 hard.How does the nature of Independent Set change in  the context of FPT and why?
Hardness of FPT problems
cc.complexity theory;parameterized complexity;fixed parameter tractable