How would you query Picasa from a Google App Engine app? Data API or Url Fetch? What are the pros and cons of using either method?
[Edit]
I would like to be able to query a specific album in Picasa and list all the photos in it.
Code examples to do this in python are much appreciated.
Your question is a little off, since the Data API is exposed through RESTful URLs, so both methods are ultimately a "URL Fetch".
The Data API works quite well, though. It gives you access to nearly all the functionality of Picasa, and responses are sent back and forth in well-formed, well-documented XML. Google's documentation for the API is very good.
If you only need access to limited publicly available content (like a photostream) then you can do this at a very basic level by just fetching the feed url and parsing that... but even for that you can get the same data with more configuration options via the Data API URLs.
I'm not sure what code samples you'd like... it really depends what you actually want to do with Picasa.