This paper studies a cognitive network where licensed primary users and unlicensed but `cognitive' secondary users share spectrum. Many system design parameters affect the joint performance, e.g., outage and capacity, seen by the two user types in such a scenario. We explore the sometimes subtle system tradeoffs that arise in such networks. To that end, we propose a new simple stochastic geometric model that captures the salient interdependencies amongst spatially distributed primary and secondary nodes. The model allows us to evaluate the performance dependencies between primary and secondary transmissions in terms of the outage probability, node density and transmission capacity. From the design perspective the key design parameters determining the joint transmission capacity and tradeoffs, are the detection radius (detection SINR threshold), decoding SINR threshold, burstiness of coverage and/or transmit powers. We show how the joint transmission capacity region can be optimized or affected by these parameters.