Consider a set of nodes distributed spatially over some region forming a network, where every node takes measurements of an underlying process. The objective is for every node in the network to estimate some parameter of interest from these measurements by cooperating with other nodes. In this work we compare the performance of four adaptive implementations. Two of the implementations are distributed and network-based; they are spatial LMS and incremental LMS. In both algorithms, the nodes share information in a cyclic manner and both algorithms differ by the amount of information shared (less information is shared in the incremental case). The two other adaptive algorithms that we study deal with centralized implementations of spatial and incremental LMS. In these latter cases, all nodes exchange data with a fusion center where the computations are performed. In the centralized approach, all nodes receive the same estimates back from the fusion center, while these estimates differ among the nodes in the distributed implementation. We analyze and compare the performance of fusion-based and network-based versions of spatial LMS and incremental LMS processing and reveal some interesting conclusions. The results indicate that incremental LMS can outperform spatial LMS, and that network-based implementations can outperform the aforementioned fusion-based solutions in some revealing ways.