OK, big topic here and one I am thick in the middle of right now, so I will share my experience, and will welcome the discussion.
First the similarities:
Both require good programming skills and logical thought.
Both are essentially platform independent these days.
Both can provide full SQL database functionality.
You can code the same simple page in both languages and the user won't be able to tell the difference.
ASP (classic) is interpreted, which means the code has to be read each time a page is called. JSP is compiled into java classes which makes for a much faster page generation.
Classic ASP (not the new .NET) has to rely on Active X, COM or other microsoft technologies to really enhance functionality of the code. JSP can bring in every java capability.
Handling email in ASP requires external components such as CDONTS or ASPMail and was tricky to implement. JavaMail for JSP was a 10 minute download and was much easier to use.
Personally, I find JSP to be much more robust than ASP. You have more tools available to you. But both will get the job done.
I just "finished" (are they really ever finished?) a major ASP site over mySQL that has close to 2500 pages of code with some pretty impressive stuff. I'm starting on a similar project using JSP now, and have the books at the ready and get frustrated with the different syntax and calls, etc. but plow through.
I wrote another pretty involved ASP site in about 72 hours once, because I was so fluent in it.
Which is better is really subjective.
A good ASP tutorial is available at www.w3schools.com
A good JSP tutorial is available from java.sun.com
There is a good article from March 2001 comparing the two technologies at sdmagazine.com, but I can't give the full URL here. You need to register and sign in, etc. It's by Jim Farley so you can search for it.
Let's here more about this one.