PageRank != a page's ranking. PageRank is a mathmatical formula used by Google to determine a page's link popularity. It is one of hundreds of ranking factors used to determine a page's ranking.
The length of a domain (i.e. number of characters in the domain name) is not a ranking factor nor should it be. It is an indicator of nothing.
Both of the domain names you use as examples have benefits. The longer domain name contains keywords you wish to rank well for which is a postive ranking factor. (However, exact match domains are no longer a benefit like they used to be). The shorter one is easy to remember and quick to type in (and is great for places like twitter where the number of characters you can use is very limited). What would be a good thing to do is make the longer domain your primary domain and have the shorter point to it. I would then 301 redirects to redirect from the shorter one to the longer one. That way you can use the shorter one when appropriate and users (and search engines) will end up at the longer domain which is your primary domain. The 301 redirect will make sure the search engines know it is the primary domain and you also won't have duplicate content issues.