Explain the differences between Server-side and Client-side code?

Server side scripting means that all the script will be executed by the server and interpreted as needed. ASP doesn't have some of the functionality like sockets, uploading, etc. For these you have to make a custom components usually in VB or VC++. Client side scripting means that the script will be executed immediately in the browser such as form field validation, clock, email validation, etc. Client side scripting is usually done in VBScript or JavaScript. Download time, browser compatibility, and visible code - since JavaScript and VBScript code is included in the HTML page, then anyone can see the code by viewing the page source. Also a possible security hazards for the client computer.

What does AspCompat="true" mean and when should I use it?

AspCompat is an aid in migrating ASP pages to ASPX pages. It defaults to false but should be set to true in any ASPX file that creates apartment-threaded COM objects--that is, COM objects registered ThreadingModel=Apartment. That includes all COM objects written with Visual Basic 6.0. AspCompat should also be set to true (regardless of threading model) if the page creates COM objects that access intrinsic ASP objects such as Request and Response. The following directive sets AspCompat to true:
<%@ Page AspCompat="true" %>
Setting AspCompat to true does two things. First, it makes intrinsic ASP objects available to the COM components by placing unmanaged wrappers around the equivalent ASP.NET objects. Second, it improves the performance of calls that the page places to apartment- threaded COM objects by ensuring that the page (actually, the thread that processes the request for the page) and the COM objects it creates share an apartment. AspCompat="true" forces ASP.NET request threads into single-threaded apartments (STAs). If those threads create COM objects marked ThreadingModel=Apartment, then the objects are created in the same STAs as the threads that created them. Without AspCompat="true," request threads run in a multithreaded apartment (MTA) and each call to an STA-based COM object incurs a performance hit when it's marshaled across apartment boundaries.
Do not set AspCompat to true if your page uses no COM objects or if it uses COM objects that don't access ASP intrinsic objects and that are registered ThreadingModel=Free or ThreadingModel=Both.