If I have 1000 external links with 50 distinct keywords, is it better to direct them all at one site or 10 different sites? The numbers are just examples.
I did something very similar to improve my SEO and it worked; I faced the same question as you're asking and my answer was to do something like:
1000 sites pushed to 30 sites. Those 30 sites pushed to 10 sites. Those 10 sites pushed to my main site.
Please note, the example I gave shows only '3' stages, in live there were about 10.
Actually, on another site, I did it again and this method worked even better:
1000 sites pushed to 30 sites.
The reason for this approach was my head saying the logic makes more sense. The reason why we link to a site is 2 fold. 1) SEO 2) We are implying that the site being linked to (destination) is the Authority. The linking site (source) is just a reference. Hence why linking like this is popular.
However, it doesn't make total sense that the Authority is the more appropriate site. Think about cars. I could have a site about cars which links to a site which lists car manufacturers. OK, the car manufacturing site is the authority, but, if I wanted to know about cars then it's actually only painting part of the picture. Going back to the car site (the source) also has a link to another authority website about how the engine works, road traffic signs etc... Well, my site is never the authority but, it's actually the most useful website as from here, I can get to what I need. Ironically, my site which only has outbound links has become the authority.
This means you have to be careful about the linking to a destination page as it doesn't mean Google will view it as the most important and ironically I have had some of my 'child' sites rank better than my main site.
So, what is better? As time goes on, I think my car example site will become more prevalent with Google but for the moment, linking many to a few, then a few, then to one is a better approach. It also gives you scope to build on your child sites as they become popular, plus, you can also 'swamp' Google (although again, I advise doing this very cautiously).
Generally this is a 'grey hat' approach (and some may even describe as black hat) and should be done carefully.