OK, so my question, and there is bias here. Why aren't you looking at JBoss app server?
Anyway, my experience with both Weblogic and Websphere is this.
1. I found Websphere much more difficult to learn and deploy applications. Basically felt like you had to jump through too many hoops to deploy. 2. Weblogic was the first App Server I ever used in 2000 and have come accross it much more than Websphere. Weblogic does a great job in making management of its app server easy with its console app and easy to deploy apps. 3. I am sure there might be a different in price. 4. In terms of market space and future job opportunities, I think Weblogic is used in more places than Websphere, (Not that this should be used as a basis of decision making, just a point)
My choice between those two app servers is Weblogic. But if I had choice of any App Server, I would choose JBoss or Glassfish over both of those because I feel they are better app servers and also FREE!!! Of course I would choose always JBoss because I like it so much that that is who I now work for.