1) Static URLs typically Rank better as far as the search engines are concerned.

2) Static URLs are always friendlier looking as far as the end users are concerned.

What the Official Google Webmaster Central Blog has to say on the issue:

a) What is a static URL?

A static URL is one that does not change, so it typically does not contain any url parameters. You can search for static URLs on Google by typing filetype:htm in the search field. Updating these kinds of pages can be time consuming, especially if the amount of information grows quickly, since every single page has to be hard-coded. This is why webmasters who deal with large, frequently updated sites like online shops, forum communities, blogs or content management systems may use dynamic URLs.

b) What is a dynamic URL?

If the content of a site is stored in a database and pulled for display on pages on demand, dynamic URLs maybe used. In that case the site serves basically as a template for the content. You can spot dynamic URLs by looking for characters like: ? = &. Dynamic URLs have the disadvantage that different URLs can have the same content. So different users might link to URLs with different parameters which have the same content. That's one reason why webmasters sometimes want to rewrite their URLs to static ones.

c) Should I try to make my dynamic URLs look static?

Following are some key points you should keep in mind while dealing with dynamic URLs:

It's quite hard to correctly create and maintain rewrites that change dynamic URLs to static-looking URLs. It's much safer to serve us the original dynamic URL and let us handle the problem of detecting and avoiding problematic parameters.If you want to rewrite your URL, please remove unnecessary parameters while maintaining a dynamic-looking URL.

If you want to serve a static URL instead of a dynamic URL you should create a static equivalent of your content.

d) Which can Googlebot read better, static or dynamic URLs?

"We've come across many webmasters who, like our friend, believed that static or static-looking URLs were an advantage for indexing and ranking their sites. This is based on the presumption that search engines have issues with crawling and analyzing URLs that include session IDs or source trackers. However, as a matter of fact, we at Google have made some progress in both areas. While static URLs might have a slight advantage in terms of clickthrough rates because users can easily read the urls, the decision to use database-driven websites does not imply a significant disadvantage in terms of indexing and ranking. Providing search engines with dynamic URLs should be favored over hiding parameters to make them look static."

by Juliane Stiller and Kaspar Szymanski, Google Search Quality Team

Search engines always face a lot of problems in creating links to dynamic content.

If you are yourself able to know these kinds of problems, you are halfway to getting your dynamic content indexed. Where ever possible, use static URLs to reference dynamic content.

If it is not possible then you must make sure that your dynamic URL is attached to by content referenced with the help of static URLs. You can also think upon making use of paid-inclusion programs.