Advantages:
1. ASP .NET Server Controls can detect the target browser’s capabilities and render themselves accordingly. No issues for compatibility issues of Browsers i.e page that might be used by both HTML 3.2 and HTML 4.0 browsers code is written in the Server Controls.
2. Newer set of controls that can be used in the same manner as any HTML control like Calender controls. Without any need of Activex Control without bringing up issues of Browser compatibility).
3. Processing would be done at the server side. In built functionality to check for few values(with Validation controls) so no need to choose between scripting language which would be incompatible with few browsers.
4. ASP .NET Server Controls have an object model different from the traditional HTML and even provide a set of properties and methods that can change the outlook and behavior of the controls.
5. ASP .NET Server Controls have higher level of abstraction. An output of an ASP .NET server control can be the result of many HTML tags that combine together to produce that control and its events. Example Gridview or Form control.
Disadvantages:
1. The control of the code is inbuilt with the web server controls so you have no much of direct control on these controls
HTML Server Controls
Advantages:
1. The HTML Server Controls follow the HTML-centric object model. Model similar to HTML
2. Here the controls can be made to interact with Client side scripting. Processing would be done at client as well as server depending on your code.
5. A HTML Server Control has similar abstraction with its corresponding HTML tag and offers no abstraction.
Disadvantages:
1. You would need to code for the browser compatibility.
2. The HTML Server Controls have no mechanism of identifying the capabilities of the client browser accessing the current page.