Does the capacitance values matter in a full wave voltage doubler?
The doubler is essentially two half-wave rectifiers. You can estimate the peak-to-peak ripple of the doubler from:

\$V_R = \frac{V_{IN(peak)}}{R_L\cdot f \cdot C}\$

Where f is the frequency (valid for Vr &lt;&lt; Vin) 

So if you are willing to have a 5% peak-to-peak ripple, then 

\$C \ge \frac{20}{R_L\cdot f}\$

This ignores the capacitance of the diodes, which may not be accurate for very low
value load output capacitors, as well as making the conservative assumption that the current is constant at peak.  



Incidentally, the photo you have shows a film capacitor on the right. Nothing wrong with that, they have a very long life, but they are relatively large for values exceeding a microfarad or so. In most applications, an electrolytic capacitor would be chosen. A typical 10uF/450V electrolytic cap is 10mm diameter and 22mm tall. A 47uF is more like 16mm diameter and 32mm tall.