What is the advantage of using many low-farad capacitors instead of a few high-farad capacitors, when trying to maximize current?
Go for the larger one. There's lots of talk about lower ESR for the smaller ones, but I checked on Digikey, and it all seems to make very little difference. Of the 1000\$\mu\$F/25V electrolytics the ones with the lowest ESR listed are 38m\$\Omega\$, USD 1.77. A 10000\$\mu\$F/25V with 50m\$\Omega\$ ESR costs USD 3. So that's not much difference. Lower is possible at a price.  

The single 10000\$\mu\$F will also take far less space than 10 \$\times\$ 1000\$\mu\$F.