We consider a multiuser diffusion-based molecular communication (MC) system where multiple spatially distributed transmitter (TX)-receiver (RX) pairs establish point-to-point communication links employing the same type of signaling molecules. To realize the full potential of such a system, an in-depth understanding of the interplay between the spatial user density and inter-user interference (IUI) and its impact on system performance in an asymptotic regime with large numbers of users is needed. In this paper, we adopt a three-dimensional (3-D) system model with multiple independent and spatially distributed point-to-point transmission links, where both the TXs and RXs are positioned according to a regular hexagonal grid, respectively. Based on this model, we first derive an expression for the channel impulse responses (CIRs) of all TX-RX links in the system. Then, we provide the maximum likelihood (ML) decision rule for the RXs and show that it reduces to a threshold-based detector. We derive an analytical expression for the corresponding detection threshold which depends on the statistics of the MC channel and the statistics of the IUI. Furthermore, we derive an analytical expression for the bit error rate (BER) and the achievable rate of a single transmission link. Finally, we propose a new performance metric, which we refer to as area rate efficiency (ARE), that captures the tradeoff between the user density and IUI. The ARE characterizes how efficiently given TX and RX areas are used for information transmission and is given in terms of bits per area unit. We show that there exists an optimal user density for maximization of the ARE. Results from particle-based and Monte Carlo simulations validate the accuracy of the expressions derived for the CIR, optimal detection threshold, BER, and ARE.