Two 4,700uF caps will generally have a lower ESR than one 10,000uF, and when I last checked the smaller cap was better value in terms of dollars/mF.
If you double the size of the filter reservoir, you will increase the pulse charge current from the transformer. This has two effects. Firstly, it will strain the UFSR diodes specified in the design, and some, usually at start up, will blow spectacularly. Secondly, the high pulse currents will heavily stress the transformer at the point in the waveform where it recharges the caps, and in turn produce more switching noise. There is a tradeoff, and the only way to push beyond this envelope is to go full regulation. Although a lot more expensive, this yields good results, IF the regulation is super fast.
Cheers,
Hugh