In metal, the electrons are forming orbitals of atoms, atoms, which are located in a tightly packed, crystalline, or crystal-like lattice with density related to this state of matter - higher than other states of matter, such as liquid, gas, or plasma. Plasma is a higher energy state, formed by deposition of energy into the structure of i.e. metal, liquid, or gas, and for this reason, the electrons are liberated from their parent atoms forming an electron-ion gas-like state, having, as a result, much lower electron density than the metal. So in the simplest form: the electron density is smaller in the plasma because its overall density (due to existing in a temporary excited state) is less than metal. Of course, I am talking here about "normal" conditions, and not these in the core of stars, etc.
The question is not very clear, Do you mean the plasma produced from the same material? If the plasma volume is large then its obvious its density will be less.
Because higher temperature(which is the difference between plasma and metal) means more kinetic energy, and hence electrons and ions take up more volume, hence reduced density. This does not mean that you cannot have plasma with density higher than solid. You can and you do, but you need to compress e.g. by lasers as in ICF or some other mechanism.
Due to very high temperature of plasma medium, the electrons and ions are randomly distributed like a gas molecules. In contrast to this, the electrons in the metals/solids are bounded by the nucleus. Due to which, the electron density can be considered higher for metals than plasma.