A "regular" <table> is not available for modification at all on the server side. As far as the server-side is concerned, it's just static text that gets output to the browser.
I would say that as a general rule, favour <table> unless you explicitly need to modify the structure of the table on the server. Using <asp:Table> means you have the overhead of running the code-behind for the table, generating the server-side control and so on. If you're not using any of that functionality, then there's no point.
Also, in general, <asp:DataTable> is typically more useful than just plain <asp:Table>, since it supports data-binding and so on.
Usually, if I just want to show/hide a single row in a table (or something) then I'll just put runat="server"
on the single <tr> that I want to control, rather than using a whole <asp:Table>.