This would require a full report from a consultant! No space for that here.
Client server computing cost of ownership really depends on how it is implemented and if that really fits the business need.
You can assume that for every tier you add, you will split out another part of the system onto another server and this will require the associated middleware. It also may increase network traffic which will require more capacity. This adds costs.
If the application is well suited to being broken ups into bits, the development costs and the cost of renewing various bits of that development will drop.
For thin clients, business rules tend to be elsewhere. Very thin clients don't even check the data you put in - it all goes to a validation server (which may or may not contain business rules - they might be in the application server tier.) Thin clients often don't need such a high spec so tend to be cheaper.
Thick clients are more likely to be powerful machines (more work to do, more cost) and will do much of the basic validation server work and may have some very basic business rules (complex ones on the application server or as constraints in the database). This means you only send usable data once over the network - lower cost there.
