I have not really used the asp.net grid component that much, only in a small project about two years ago. I never had any performance problems then, but the amount of data in that project was quite small. I do not think we ever displayed more than 100 rows or so of data with 8-10 columns. So hopefully someone else can help you out with feedback on the asp.net grid.
As for the Silverlight grid, so far I have had no performance issues. I have tried using it with several thousands of rows and it is quite fast. The bottle neck when displaying collections that large is the client/server communication (I use WCF), and that of course has nothing to do with the components. I believe that there used to be some performance issues when using large amounts of columns
, but that has been greatly improved with the column virtualization feature which was added in the latest release (I think, or maybe it was even earlier). You have probably seen it already, but there is a good demo of the virtualization features here: