Actual answer: Silverlight MAY replace Asp.net, but it will not . This is how to say: Trucks / buses can replace cars, but they will not. They all serve a different purpose.
They will both thrive in their field.
These two technologies should live side by side with joy. They are intended for different purposes, and they are likely to remain so. The things that will change / format them are browsers. With the upcoming HTML5, even Microsoft recognizes that Silverlight may not survive.
Also consider SEO and content indexing. To my knowledge, Silverlight content is not indexed. So there was no flash memory that is indexed today. Silverlight may also be at the same point, but indexing such dynamic content is much more difficult for search providers.
My opinion is that Silverlight will thrive in a very rich client (or web client) web connection of applications, as in business applications and other interfaces that require high interactivity and complex presentation.
Silverlight is much better suited for these purposes than Asp.net. Give or take Ajax at Asp.net. HTML5 will make things a little better, but it's still just HTML. Therefore, do not expect entire websites to function as Silverlight applications (think of online games, video and image editing solutions, online casinos, animated animated content, etc.). This is Silverlight. Imagine doing the same with HTML. That will be a problem!
Microsft (my personal opinion) did a very poor job evangelizing Silverlight because they tried to make it compatible with Flash video players, etc. Try asking developers what comes to their minds when someone mentions Silverlight. Many of them do not really understand why this is necessary. And this is a Microsoft bug because it does not make it very clear.
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