Firstly, having 50 links off your home page to another site is not the normal and google will perhaps think you are a doorway page. Think of it this way, if you are saying to visitors "OH, you don't want this page, go here..." fifty times on your home page, then the usefullness of the site is questionable and Google may think why should I bother ever showing it?
However, if you have a few external links to related sites with topics your site doesn't cover, then that could be good.
Apart from that, in simple terms you have a pr allocated to a page, lets say pr5. If you have 10 links off the page, in theory the pr is divided by 10 and given to each link to carry across to the respective page. So if you have 50, you give 1/50th to each page on the other site you mentioned. If you only have one link then you get all the pr going across to that one page. If that one page then distributes the pr to the other 49 pages, in theory the effect is almost the same as 50 links from your other site..... but it isn't....because in my opinion external links are treated differently to links to the same domain and the 49 pages are now two clicks away rather than one.
Plus a whole bunch of other stuff may apply! Google says 100 links is the most they want to see, though they will follow more but the pr flow probably gets too diluted.