There are a lof of websites that use some sort of framework that doesn't show the .jsp extension (I would think probably most of them actually). So only looking at the extension of the url isn't a correct way of determining whether the website uses java or not.
Java has been around for a lot more years than .net. But there isn't anything that makes .net more modern than java. Also, there are a lot more software libraries and frameworks around that you can choose from (and a lot of them are open source and you can use them for free). The reason why .net is popular is, I think, that it comes with a tool (Visual Studio) that makes it easy to create a simple website really fast. But if you use it that way, the quality of your work will be very low, and if there is something wrong with it, you won't be able to fix it because you haven't got a clue what you have done. To build a decent website the amount of work in java or in .net is about the same.
If you want to become web developer then you can try an emergin Open Source Technology "Ruby on Rails", which is gaining awsome popularity now a days. Even "Ruby" declared TIOBE's Programming Language of 2006! You can check it here:- http://www.tiobe.com/tpci.htm