You can get the basic idea by considering the stress-strain equation as an example. Higher young modulus means that either high stress or lower strain value or both. So, you can basically think that the higher young modulus the material has, the stiffer it gets. For instance, the rubber has lower stiffness since it can be deformed elastically more than steel or diamond. That is, it has lower stiffness.
There are some exceptions of course, but what I have mentioned above is the rule of thumb in case of fundamental mechanical property evaluation.
I feel the material with higher Young's modulus has more stiffness than the material with lower Young's modulus..the Young's modulus is the stress - strain characteristics of material..the material with higher Young's modulus take larger load with less strain as compared to the material with lower Young's modulus..also, the stiffness is the material resistance against the applied pressure on it ..so stiffness and Young's modulus is interrelated properties of any material..this phenomenon is nicely explained by Mr.Burak..