If we take neutron star material at say a density of $sim 10^{17}$ kg/m$^{3}$ the neutrons have an internal kinetic energy density of $3 times 10^{32}$ J/m$^{3}$. So even in a teaspoonful (say 1 cc), there is $3times10^{26}$ J of kinetic energy (similar to what the Sun emits in a second, or 10 billion or so H-bombs) and this will be released instantaneously.
The energy is in the form of around $10^{38}$ neutrons travelling at around 0.1-0.2$c$. So roughly speaking it is like half the neutrons (about 50 million tonnes) travelling at 0.1$c$ ploughing into the Earth. If I have done my Maths right, that is roughly equivalent to a 30 km radius near-earth asteroid hitting the Earth at 30 km/s.
So this material would instantly vapourise and take a large chunk of the Earth with it, probably destroying most of life on Earth.
The situation for a white dwarf is much less extreme. The density would be more like $10^{9}$ kg/m$^3$ and the energy density more like $10^{22}$ J/m$^3$ - so 10 orders of magnitude less kinetic energy density. Nevertheless that is still $10^{16}$ J, which is like a 2.5 megatonne H-bomb.
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