In topical client server system, the server machine is much more powerful than the client i.e it processor is faster, it may have multiple processor and it has more memory and disk capacity.
Consider instead a scenario where client and server machine having exactly the same power. Would it make sense to build a client server in such scenario? Why? Which scenario would be better suited to a data server architecture?

The whole idea of building a client server architecture as you rightly stated is because server hardware maybe much better than the client hardware. However another important factor for using a client server architecture is because you want to be able to run the client and server over a different network or remotely. Take for example you are in the Lagos and the Machine you want to interact with is in Abuja, even if both have the same processing power. It makes much more sense to use a client-server approach. So i think you need to explain what you want more clearly in your initial posting.
This are some of the reasons to use client-server architecture:
a. Server hardware has unlimited or more resources(CPU,Memory,Storage).
b. Need to work remotely or over a network.
c. The data in question can only be secure if its on a central server. E.g Some applications require additional security and does not make sense to install it on every client pc. Banking app should not be installed on all the cashier pc.
d. The operating system environment may also neccessiate you run a client-server arhcitecture.

And to add to Myhelper123, a client server architecture does not necessarily mean the server is more powerful (At least not in all cases). And your scenario where the client has exactly the same processing power with the server, the best way to use that is in Peer to Peer networks. Where each node in the network acts as both a client and a server.

Thanks@Seunthamos.....I still have one more sir!
Instead of storing share structure in share memory, an alternative architecture would be to store them in a local memory of a special process and access the store data by inter process communication with the process, what would be the draw back of such an architecture?
Pls help me out

Myhelper123:
Thanks@Seunthamos.....I still have one more sir!

Instead of storing share structure in share
memory, an alternative architecture would be to
store them in a local memory of a special process
and access the store data by inter process
communication with the process, what would be
the draw back of such an architecture?

Pls help me out

I assume what you are describing here is a message queue(non socket based). The advantages of a message queue is that their is very little latency(time to fetch the data over the network) as the application can just request data from the necessary process. However it has significant drawbacks like data corruption(were the data in the storage process is corrupted). Also the architecture needs to be properly done or else there maybe race condition scenerios where multiple processes or threads try to reach the data in the storage process and are blocked. In order to understand what you want better i would need you to describe examples of this application.

Example is Database

Example is Database Management System DBMS