This paper considers sparse device activity detection for cellular machine-type communications with non-orthogonal signatures using the approximate message passing algorithm. This paper compares two network architectures, massive multiple-input multiple-output (MIMO) and cooperative MIMO, in terms of their effectiveness in overcoming inter-cell interference. In the massive MIMO architecture, each base station (BS) detects only the users from its own cell while treating inter-cell interference as noise. In the cooperative MIMO architecture, each BS detects the users from neighboring cells as well; the detection results are then forwarded in the form of log-likelihood ratio (LLR) to a central unit where final decisions are made. This paper analytically characterizes the probabilities of false alarm and missed detection for both architectures. Numerical results validate the analytic characterization and show that as the number of antennas increases, a massive MIMO system effectively drives the detection error to zero, while as the cooperation size increases, the cooperative MIMO architecture mainly improves the cell-edge user performance. Moreover, this paper studies the effect of LLR quantization to account for the finite-capacity fronthaul. Numerical simulations of a practical scenario suggest that in that specific case cooperating three BSs in a cooperative MIMO system achieves about the same cell-edge detection reliability as a non-cooperative massive MIMO system with four times the number of antennas per BS.