I have two client-server protocols which perform the same function but they have different complexities in time (in terms of number of operations) and space (in terms of number of objects of same type). The size on which are based the complexities is $n$.
In the fist one, the server has to send only one object and the client has to perform $n$ operations.
In the second one, the server has to send $\log n$ objects and the client has to perform $\log n$ operations.
What is the best algorithm ? Does it depend on the environment of execution ?