Well you either stabilize particles electrostatically or sterically (or both?). In general polymers are used to induce steric stability while small charged molecules are used to impart electrostatic stability.
It depends on the size and charge of stabilizer’s molecule. It’s well-known fact, that the stability of colloids depends on repulsion and attraction balance. The attraction forces (for example, van der Waals ones) cause nanoparticle aggregation; in the stable sol the repulsion needs to be more strong. There are two main mechanisms of repulsion: electrostatic and steric ones. First is produced by formation of electrical double layer around nanoparticles, it occurs when two nanoparticles approach each other overlapping their double layers. This mechanism is good, but very sensitive to many factors, such as ionic strength of dispersion media, presence of other charged molecules or particles (surfaces).. The thickness of double layer drastically decreases at high ionic concentration, nanoparticles approach too close and the attraction takes place. As a rule, the most of real fluids (biological or technical) are strong electrolytes, containing a lot of active components that can cause instability of sols and aggregation of particles. That’s why the second, steric mechanism has always be used for real systems, when the repulsion is produced by surfactants or polymers, which form the protective layers on the surface of nanoparticles – it’s prevent their approach to attraction due to the energetically unfavorable interaction of hydrated chains (common steric stabilizer has high hydrophilicity).
As Omar correctly explains, there are 2 routes for stabilization of small systems - charge stabilization (often, but incorrectly called electrostatic) and steric stabilization. For some systems, e.g. magnetite, only steric stabilization will work as the long range magnetic forces easily overcome any charge effects. BTW, van der Waals forces are always attractive for entities of the same chemistry. So, the nature/chemistry of the material is important too in deciding which is appropriate. Also, one needs to decide what happens next. In the ceramics industry one can keep the particles separate in the casting slip but then the particles need to be brought together and that may entail the removal of any polymer layer - and this could prove difficult.
The polymer stabilized metal nanoparticles are more stable than the NPs stabilized by small molecules such as citrate or CTAB.
The polymer stabilized metal NPs can be freeze dried and stored for long time, and it can be soluble when dissolving in water (any suitable solvent).
In the case of small molecule stabilized metal NPs, they are more stable in solution form with out any doubt, but they may involve in aggregation when freeze drying, and it will not dissolve when try to reconstitute in solution form.
In conclusion, polymer stabilized metal NPs are more stable in solid powder form for longer period (even 1 to 2 year depending on polymer stability and degradation rate).....
It is obvious that the steric stabilizers (polymers) can stabilize the nanoparticles surface more effectively than the small molecule due to their multiple functionality, anchoring ability, malleability, complete and smooth coverage of the active surface by adsorption. In addition, polymeric stabilizers can act as both the steric as well as ionic stabilizer if they have suitable ionic functionality in it.
There can not be a general answer for this question since the type of nano particle and the nature of the stabilizing agent determines the overall stability of the nps. Unless a detailed investigation is made by employing a number of stabilizing agents with a given nano particle, a general conclusion can not be arrived at.